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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Discrete Probability Distributions\nTerms & Definitions"]
[]
[]
[]
[null,"Excel Business Statistics 23"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 7: Cross Tabulation, Visualizations, AND Logical Tests, Simpson’s Paradox"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Using Formulas to Build\nDiscrete Probability Distributions\nto Help Make Business Decisions"]
[]
[]
[]
[null,"Excel Business Statistics 24"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 24: Build Discrete Probability Distribution, Expected Value, S. Deviation"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Power Query to Import Excel Data to Build PivotTable\nDiscrete Probability Distribution"]
[]
[]
[]
[null,"Excel Business Statistics 25"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 24: Build Discrete Probability Distribution, Expected Value, S. Deviation"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Accounting & Finance\nDiscrete Probability Distribution Examples"]
[]
[]
[]
[null,"Excel Business Statistics 26"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 24: Build Discrete Probability Distribution, Expected Value, S. Deviation"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Binomial Probability Distributions\n& Amazing\nBINOM.DIST.RANGE Function"]
[]
[]
[]
[null,"Excel Business Statistics 27"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 24: Build Discrete Probability Distribution, Expected Value, S. Deviation"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"Poisson Discrete\nProabability Distribution\nand POISSON.DIST Function"]
[]
[]
[]
[null,"Excel Business Statistics 28"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 24: Build Discrete Probability Distribution, Expected Value, S. Deviation"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

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[]
[null,"Excel Business\nStatistical Analysis:"]
[]
[]
[]
[]
[]
[null,"HYPGEOM.DIST Function\nand\nHypergeometric Distribution"]
[]
[]
[]
[null,"Excel Business Statistics 29"]
[]
[]
[]
[]
[null,"Excel Statistical Analysis 24: Build Discrete Probability Distribution, Expected Value, S. Deviation"]
[null,{"$f":"LEN(B17)","v":100}]
[null,null,{"$f":"LEN(C18)","v":0}]
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[]
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[null,null,null,null,null,null,null,"Microsoft 365 Excel"]

{"sheet":"Print Notes From Excel File","index":7,"n_rows":119,"n_cols":15,"rows_kept":119,"cut":false,"hidden":false,"merged":[[86,0,86,12],[87,0,87,12]]}
["Notes from Excel Workbook File \"Ch05-ESA.xlsm\":"]
[]
["Chapter 4 Terms:"]
["Probability"]
[" E = Event, P = Probability, then P(E) = A Number between 0 and 1, inclusive."]
["Estimate of the unknown future"]
["Random Experiment:"]
["1) Well Defined Outcomes"]
["2) Any single Trial only one outcome can occur"]
["3) Outcome occurs by chance"]
["Multi-Step Experiment:"]
["Random Experiment with more than 1 Step/Trial"]
["Sample Point"]
["Sample Point = Experimental Outcome"]
["Sample Space"]
["List of all Possible Sample Points/Experimental Outcomes"]
["{Total Number Sample Points} for Multi-Step Experiment:"]
["k = Number of Steps"]
["nk = Outcomes for particular Step"]
["{Total Number Sample Points} = n1 + n2 + … nk "]
["If number of outcomes is same for each Step, {Total Number Sample Points} = n^k"]
["Assigning Probability"]
["Classical = All Sample Points are equally likely"]
["Relative Frequency = Data from past is Relative Frequency Table that has categories which are:"]
["Mutually Exclusive (no item fits into more than one category) and Collectively Exhaustive (enough categories to count everything)."]
["Subjective = Outcomes not equally likely, Little past data, Use best information you can find but it will be your personal belief"]
["Requirements for Assigning Probabilities:"]
["1) All Sample Points must have a probability between 0 and 1, inclusive"]
["2) Sum of all Sample Point Probabilities = 1"]
["Event"]
["Collection of 1 or more Sample Points"]
["Probability of an Event"]
["Sum of the probabilities of the  Sample Points in the Event"]
[]
["Chapter 5:"]
["Random Variables"]
["A numerical description of the outcome of an experiment"]
["Discrete Random Variables"]
["May assume either: a finite number of values like: 1, 2, 3 or an infinite sequence of numbers like 1, 2, 3… (Gaps between numbers)"]
["Continuous Random Variables"]
["May assume any numerical value in an interval or collection of intervals. Depends on measuring instrument"]
["Many possible numbers between 1 & 2. \"No Gaps\""]
["Probability Distributions"]
["A description/Presentation of how the probabilities are distributed over the values of the random variable."]
["Models"]
["Random Variables and Probability Distributions are models for populations of data that we can use to estimate the unknown future."]
["Discrete Probability Distributions"]
["A description/Presentation of how the probabilities are distributed over the values of a discrete random variable."]
["Discrete Probability Function",null,null,null,null,null,null,null,null,null,null,null,null,null,"                              "]
["A probability function, f(x) or P(x), that provides the probability for each value that the discrete random variable can assume."]
["Requirements for f(x) or P(x)",null,null,null,null,null,null,null,null,null,null,null,null,null,"                              "]
["f(x) = P(x) >= 0 AND ∑f(x) = ∑P(x) = 1"]
["Methods for creating Discrete Probability Distributions:",null,null,null,null,null,null,null,null,null,null,null,null,null,"                              "]
["Classical, Relative Frequency (for large data sets it is called Empirical Discrete Distribution) and Subjective"]
["Advantage of Probability Distributions?"]
["Once you have the table, it is easy to calculate probabilities for a variety of Events!!!"]
["Steps for building a Discrete Probability Distribution:"]
["1) Define Random Variable"]
["2) Build Frequency Distribution"]
["3) Calculate Relative Frequency - P(x) = f(x)"]
["4) Check Requirement #1: f(x) >= 0 , Check Requirement #2: Σf(x) = 1"]
["5) Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["6) Make predictions"]
["Expected Value for a  Discrete Random Variables",null,null,null,null,null,null,null,null,null,null,null,null,null,"                              "]
["E(x) = µ = Weighted Average = ∑x*f(x) = ∑x*P(x), use: =SUMPRODUCT(XRange,P(x)Range)"]
["Variance and Standard Deviation for a Discrete Random Variables"]
["Var = ∑(x-E(x))^2*P(x), use: =SUMPRODUCT((Xrange-E(x))^2,P(x)Range)"]
["SD = SQRT(∑(x-E(x))^2*P(x)), use: =SQRT(SUMPRODUCT((Xrange-E(x))^2,P(x)Range))"]
["Binomial Experiment"]
["Requirements:"]
["1) Fixed Number of Trials, n = # Trials"]
["2) Each Trial can only result in two outcomes: Success or Failure"]
["3) Probability of success is the same for each trial"]
["4) Trials are independent (one does not affect the next)"]
["Binomial Probability Function"]
["f(x) = P(x) = n!/(x!*(n-x)!)*p^x*(1-p)^(n-x)"]
["In Excel use: BINOM.DIST(x,n,p,cumulative)"]
["x = Number of Successes = Discrete Random Variable = number_s"]
["n = Total Steps/Trials = trials"]
["p = Probability of Success = probability_s"]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x or height of column in Column Chart"]
["OR"]
["cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]
["In Excel use: BINOM.DIST.RANGE(n,p,x_low,x_high)"]
["n = Total Steps/Trials = trials"]
["p = Probability of Success = probability_s"]
["x_low = Number of Successes for first x = Discrete Random Variable = number_s. If you use this argument and NOT the [number2] argument, the function will calculate the probability for the x value, which is also the height of the column if you plot all x vales in a Column Chart."]
["x_high = Number of Successes for second x = Discrete Random Variable = [number_s2]. If you use this argument and the number_s argument, the function calculates the total probability between the first x and second x, inclusive."]
["Expected Value and Variance and Standard Deviation for a Binomial Distribution"]
["E(x) = µ = mean n*p"]
["Standard Deviation = s = SQRT(n*p*(1-p))"]
["Poisson Distribution"]
["Poisson Probability Distribution can be used to estimate the number of occurrences over a specified interval of time or space"]
["Discrete Random Variable = x = Number of occurrences over a specified interval of time or space."]
["Good for number of  arrivals in waiting line situations over a certain time period (like 15 mins)"]
["Good for number of repairs needed over a distance of road or pipe"]
["Properties (Requirements) of a Poisson Experiment:"]
["1) The probability of an occurrence is the same for any two intervals of equal length"]
["2) The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval"]
["3) Mean = Variance (observed from calculations made off of source data)"]
["f(x) = P(x) = the probability of x occurrences in an interval = height of column when you plot column chart."]
["Discrete Random Variable = x = Number of occurrences over a specified interval of time or space."]
["No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gest quite small."]
["Mean = µ = Calculated from past data"]
["e = constant = 2.71828 = =EXP(1) in Excel"]
["In Excel use: POISSON.DIST(x,mean,cumulative)"]
["x = Number of occurrences over a specified interval of time or space = Discrete Random Variable"]
["mean = µ = Calculated from past data"]
["cumulative = 0 for exactly x OR 1 for less than or equal to x"]
["Hypergeometric Distribution"]
["Similar to Binomial Distribution except: 1) the trails are not independent AND 2) the probability of success changes from trial to trial."]
["In Excel use: HYPGEOM.DIST(x,n,population_s,number_pop,cumulative)"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s"]
["n = Trials/Steps in Experiment = Sample Size = number_sample"]
["Number Successes in Pop. =  population_s"]
["Population Size = number_pop"]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x"]
["OR"]
["cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]

{"sheet":"Print B","index":8,"n_rows":38,"n_cols":9,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["Binomial Example in Excel:"]
["An insurance agent has appointments with 4 clients tomorrow."]
["From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes"]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = Appointments",null,null,null,4]
["p = Prob of Success =",null,null,null,0.2]
[{"$f":"\"Random Discrete Variable = x = # Sales in \"&E10&\" Tries\"","v":"Random Discrete Variable = x = # Sales in 4 Tries"}]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"SUMPRODUCT(A25:A29,B25:B29)","v":0.79999999999999982},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E13:E16),COLUMN(E13:E16),4)&\": \"&_xlfn.FORMULATEXT(E13:E16),\"\")","v":"E13: =SUMPRODUCT(A25:A29,B25:B29)"}]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"E10*E11","v":0.8},null,"E14: =E10*E11"]
["Standard Deviation = s =",null,null,null,{"$f":"SQRT(SUMPRODUCT((A25:A29-E13)^2,B25:B29))","v":0.79999999999999993},null,"E15: =SQRT(SUMPRODUCT((A25:A29-E13)^2,B25:B29))"]
["Standard Deviation = s =",null,null,null,{"$f":"SQRT(E10*E11*(1-E11))","v":0.8},null,"E16: =SQRT(E10*E11*(1-E11))"]
[]
[]
[]
[]
[null,null,"X","P(X)","P(X)"]
["Math Formula >",null,3,{"$f":"\"P(x = \"&C22&\")\"","v":"P(x = 3)"},{"$f":"COMBIN(E10,C22)*E11^C22*(1-E11)^(E10-C22)","v":2.5600000000000008E-2},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E22),COLUMN(E22),4)&\": \"&_xlfn.FORMULATEXT(E22),\"\")","v":"E22: =COMBIN(E10,C22)*E11^C22*(1-E11)^(E10-C22)"}]
[]
["X","P(x) = f(x)"]
[0,{"$f":"_xlfn.BINOM.DIST.RANGE(E10,E11,A25:A29)","v":0.40959999999999996},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B25),COLUMN(B25),4)&\": \"&_xlfn.FORMULATEXT(B25),\"\")","v":"B25: =BINOM.DIST.RANGE(E10,E11,A25:A29)"}]
[1,0.40959999999999996]
[2,0.15359999999999996]
[3,2.5600000000000005E-2]
[4,1.6000000000000005E-3]
["Total",{"$f":"SUM(B25:B29)","v":0.99999999999999989}]
[]
["P(X)","SUM","P(X)","X Lower","X Upper"]
[{"$f":"\"P(x = \"&D33&\")\"","v":"P(x = 3)"},{"$f":"SUM(B28)","v":2.5600000000000005E-2},{"$f":"_xlfn.BINOM.DIST.RANGE(E10,E11,D33:D37,E33:E37)","v":2.5600000000000005E-2},3,3,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B33:B38),COLUMN(B33:B38),4)&\": \"&_xlfn.FORMULATEXT(B33:B38),\"\")","v":"B33: =SUM(B28)"},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C33),COLUMN(C33),4)&\": \"&_xlfn.FORMULATEXT(C33),\"\")","v":"C33: =BINOM.DIST.RANGE(E10,E11,D33:D37,E33:E37)"}]
[{"$f":"\"P(x <= \"&D34&\")\"","v":"P(x <= 0)"},{"$f":"SUM(B25:B28)","v":0.99839999999999984},0.99839999999999995,0,3,null,"B34: =SUM(B25:B28)"]
[{"$f":"\"P(x > \"&D35&\")\"","v":"P(x > 4)"},{"$f":"SUM(B29)","v":1.6000000000000005E-3},1.6000000000000005E-3,4,4,null,"B35: =SUM(B29)"]
[{"$f":"\"P(x >= \"&D36&\")\"","v":"P(x >= 3)"},{"$f":"SUM(B28:B29)","v":2.7200000000000005E-2},2.7200000000000016E-2,3,4,null,"B36: =SUM(B28:B29)"]
[{"$f":"\"P(x < \"&D37&\")\"","v":"P(x < 0)"},{"$f":"SUM(B25:B27)","v":0.97279999999999989},0.9728,0,2,null,"B37: =SUM(B25:B27)"]
[{"$f":"\"P(x <= \"&D38&\")\"","v":"P(x <= 3)"},{"$f":"SUM(B25:B28)","v":0.99839999999999984},{"$f":"_xlfn.BINOM.DIST(D38,E10,E11,1)","v":0.99839999999999995},3,null,null,"B38: =SUM(B25:B28)",null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C38),COLUMN(C38),4)&\": \"&_xlfn.FORMULATEXT(C38),\"\")","v":"C38: =BINOM.DIST(D38,E10,E11,1)"}]

{"sheet":"Print P","index":9,"n_rows":29,"n_cols":14,"rows_kept":29,"cut":false,"hidden":false,"merged":[]}
["Poisson Excel in Excel:"]
[{"$f":"\"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = \"&ROUND(B4,2)","v":"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"}]
[]
["Mean",3.8796934865900381]
["Variance",3.7546870225418991]
[]
["X = Arrivals During 1 min","Poisson P(X)"]
[0,{"$f":"_xlfn.POISSON.DIST(A8:A23,B4,0)","v":2.0657155906734028E-2},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(B8:B24),\"\")","v":"=POISSON.DIST(A8:A23,B4,0)"}]
[1,8.0143433222830948E-2,null,""]
[2,0.15546597793379047,null,""]
[3,0.20105344732535915,null,""]
[4,0.19500643751116731,null,""]
[5,0.1513130410910406,null,""]
[6,9.7841369992840155E-2,null,""]
[7,5.422778941146688E-2,null,""]
[8,2.6298400171480534E-2,null,""]
[9,1.1336636872559033E-2,null,""]
[10,4.3982676234303759E-3,null,""]
[11,1.5512663864456957E-3,null,""]
[12,5.0153650795495307E-4,null,""]
[13,1.4967753255384184E-4,null,""]
[14,4.1478782009857719E-5,null,""]
[15,1.0728330693022202E-5,null,""]
["Total",{"$f":"SUM(B8:B23)","v":0.99999664460235693},null,"=SUM(B8:B23)"]
[]
["Low X","High X",null,null,"SUM","POISSON","Formula"]
[null,0,null,{"$f":"\"P(\"&B27&\")\"","v":"P(0)"},{"$f":"SUM(B8)","v":2.0657155906734028E-2},{"$f":"_xlfn.POISSON.DIST(B27,B4,0)","v":2.0657155906734028E-2},{"$f":"B4^B27*EXP(1)^-B4/FACT(B27)","v":2.0657155906734032E-2},null,{"$f":"IF(_xlfn.ISFORMULA(E27),_xlfn.FORMULATEXT(E27),\"\")","v":"=SUM(B8)"},null,{"$f":"IF(_xlfn.ISFORMULA(F27),_xlfn.FORMULATEXT(F27),\"\")","v":"=POISSON.DIST(B27,B4,0)"},null,null,{"$f":"IF(_xlfn.ISFORMULA(G27),_xlfn.FORMULATEXT(G27),\"\")","v":"=B4^B27*EXP(1)^-B4/FACT(B27)"}]
[3,5,null,{"$f":"\"P(\"&A28&\" <= No. Arvls. <= \"&B28&\")\"","v":"P(3 <= No. Arvls. <= 5)"},{"$f":"SUM(B11:B13)","v":0.54737292592756703},{"$f":"_xlfn.POISSON.DIST(B28,B4,1)-_xlfn.POISSON.DIST(A28-1,B4,1)","v":0.54737292592756703},null,null,{"$f":"IF(_xlfn.ISFORMULA(E28),_xlfn.FORMULATEXT(E28),\"\")","v":"=SUM(B11:B13)"},null,{"$f":"IF(_xlfn.ISFORMULA(F28),_xlfn.FORMULATEXT(F28),\"\")","v":"=POISSON.DIST(B28,B4,1)-POISSON.DIST(A28-1,B4,1)"}]
[2,null,null,{"$f":"\"P( No. Arvls > \"&A29&\")\"","v":"P( No. Arvls > 2)"},{"$f":"SUM(B11:B23)","v":0.74373007753900144},{"$f":"1-_xlfn.POISSON.DIST(A29,B4,1)","v":0.74373343293664451},null,null,{"$f":"IF(_xlfn.ISFORMULA(E29),_xlfn.FORMULATEXT(E29),\"\")","v":"=SUM(B11:B23)"},null,{"$f":"IF(_xlfn.ISFORMULA(F29),_xlfn.FORMULATEXT(F29),\"\")","v":"=1-POISSON.DIST(A29,B4,1)"}]

{"sheet":"Print HG","index":10,"n_rows":134,"n_cols":13,"rows_kept":134,"cut":false,"hidden":false,"merged":[[89,1,89,13]]}
[]
[null,"Hypergeometric Distribution"]
[null,"Similar to Binomial Distribution except: 1) the trails are not independent AND 2) the probability of success changes from trial to trial."]
[null,"In Excel use: HYPGEOM.DIST(x,n,population_s,number_pop,cumulative)"]
[null,"x = Number of Successes in Sample = Discrete Random Variable = sample_s"]
[null,"n = Trials/Steps in Experiment = Sample Size = number_sample"]
[null,"Number Successes in Pop. =  population_s"]
[null,"Population Size = number_pop"]
[null,"cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x"]
[null,"OR"]
[null,"cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]
[]
[null,"Example 1:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Goal: Calculate the probability that you can pull 2 straight Queens from a deck of cards (without replacement)?"]
[]
[null,"Experiment variables:"]
[null,"Population size = # of cards in deck = number_pop =",null,null,null,null,null,null,null,null,null,null,52]
[null,"Successes in population = # of Queen cards in population = population_s =",null,null,null,null,null,null,null,null,null,null,4]
[null,"n = Fixed number of trials = sample size = # of cards pulled = number_sample =",null,null,null,null,null,null,null,null,null,null,2]
[null,"X = Random Discrete Variable that counts successes in sample = # of Queen cards selected in sample = sample_s =",null,null,null,null,null,null,null,null,null,null,2]
[]
[null,"Goal: P(Pull 2 straight Queens from deck of cards without replacement) ="]
[]
[null,null,"This means the sample space will change and the events are not independent."]
[null,null,"We will have to use Conditional Probability and the probability of success is NOT the same for each trial."]
[]
[null,null,"Because there is only one sample point, we can manually calculate it this way:"]
[]
[null,null,"Sample Points =",null,null,null,{"$f":"COMBIN(M30,M31)","v":1},null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G40:G43),\"\")","v":"=COMBIN(M30,M31)"}]
[null,null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,{"$f":"4/52*(4-1)/(52-1)","v":4.5248868778280547E-3},null,null,null,"=4/52*(4-1)/(52-1)"]
[null,null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,{"$f":"M29/M28*(M29-1)/(M28-1)","v":4.5248868778280547E-3},null,null,null,"=M29/M28*(M29-1)/(M28-1)"]
[null,null,"P(Q2 AND Q1) =",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(M31,M30,M29,M28,0)","v":4.5248868778280521E-3},null,null,null,"=HYPGEOM.DIST(M31,M30,M29,M28,0)"]
[]
[]
[null,"Example 2:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Goal: Calculate the probability that you can pull 2 Face Cards in 5 tries from a deck of cards (without replacement)?"]
[]
[null,"Experiment variables:"]
[null,"Population size = # of cards in deck = number_pop =",null,null,null,null,null,null,null,null,null,null,52]
[null,"Successes in population = # of Queen cards in population = population_s =",null,null,null,null,null,null,null,null,null,null,12]
[null,"n = Fixed number of trials = sample size = # of cards pulled = number_sample =",null,null,null,null,null,null,null,null,null,null,5]
[null,"X = Random Discrete Variable that counts successes in sample = # of Queen cards selected in sample = sample_s =",null,null,null,null,null,null,null,null,null,null,2]
[]
[null,"Goal: P(Pull Queens in 5 tries from deck of cards without replacement) ="]
[]
[null,null,"Sample space will change and the events are not independent."]
[null,null,"Must use Conditional Probability. The probability of success is NOT the same for each trial."]
[]
[null,null,"But this event has many sample points:"]
[]
[null,null,"Sample Points =",null,null,null,{"$f":"COMBIN(M63,M64)","v":10},null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G73:G75),\"\")","v":"=COMBIN(M63,M64)"}]
[null,null,"P(2 Face Cards in 5 Tries) =",null,null,null,{"$f":"SUM(H78:H87)","v":0.25090036014405764},null,null,null,"=SUM(H78:H87)"]
[null,null,"P(2 Face Cards in 5 Tries) =",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(M64,M63,M62,M61,0)","v":0.2509003601440577},null,null,null,"=HYPGEOM.DIST(M64,M63,M62,M61,0)"]
[]
[null,"Sample Point","Step 1","Step 2","Step 3","Step 4","Step 5","Prob."]
[null,{"$f":"_xlfn.SEQUENCE(G73)","v":1},"F","F","NF","NF","NF",{"$f":"12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48","v":2.5090036014405754E-2},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H78:H87),\"\")","v":"=12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48"}]
[null,2,"F","NF","F","NF","NF",{"$f":"12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48"]
[null,3,"F","NF","NF","F","NF",{"$f":"12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48"]
[null,4,"F","NF","NF","NF","F",{"$f":"12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48"]
[null,5,"NF","F","F","NF","NF",{"$f":"(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48"]
[null,6,"NF","F","NF","F","NF",{"$f":"(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48"]
[null,7,"NF","F","NF","NF","F",{"$f":"(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48"]
[null,8,"NF","NF","F","F","NF",{"$f":"(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48"]
[null,9,"NF","NF","F","NF","F",{"$f":"(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48","v":2.5090036014405761E-2},null,"=(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48"]
[null,10,"NF","NF","NF","F","F",{"$f":"(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48"]
[]
[null,"Example 3:"]
[null,"For the experiment of pulling 5 cards from deck of cards without replacement, and the X Discrete Variable = # of Face Cards pulled, here are the probabilities for all possible X values:"]
[]
[null,"X = # Face Cards","P(X)",null,"Experiment variables:"]
[null,{"$f":"_xlfn.SEQUENCE(M63+1,,0)","v":0},{"$f":"_xlfn.HYPGEOM.DIST(_xlfn.ANCHORARRAY(B93),M63,M62,M61,0)","v":0.25318127250900352},null,"Population size = number_pop =",null,null,null,null,52,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(C93),\"\")","v":"=HYPGEOM.DIST(B93#,M63,M62,M61,0)"}]
[null,1,0.42196878751500583,null,"Successes in population = population_s =",null,null,null,null,12]
[null,2,0.2509003601440577,null,"n = Fixed number of trials = number_sample =",null,null,null,null,5]
[null,3,6.6026410564225743E-2,null,"X = counts successes in sample =  sample_s =",null,null,null,null,2]
[null,4,7.6184319881798905E-3]
[null,5,3.047372795271953E-4]
[null,"Total",{"$f":"SUM(_xlfn.ANCHORARRAY(C93))","v":0.99999999999999989},null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(C99),\"\")","v":"=SUM(C93#)"}]
[]
[null,"Example 4:"]
[null,"Calculate the probability of getting 0 Face cards OR 1 face card OR 2 face cards in 5 tries:"]
[null,"X","P(X)",{"$f":"\"P(x<=\"&B104&\")\"","v":"P(x<=2)"}]
[null,2,{"$f":"\"P(x<=\"&B104&\")\"","v":"P(x<=2)"},{"$f":"SUM(C93:C95)","v":0.92605042016806705},null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D104:D105),\"\")","v":"=SUM(C93:C95)"}]
[null,2,{"$f":"\"P(x<=\"&B105&\")\"","v":"P(x<=2)"},{"$f":"_xlfn.HYPGEOM.DIST(J96,J95,J94,J93,1)","v":0.92605042016806716},null,null,"=HYPGEOM.DIST(J96,J95,J94,J93,1)"]
[]
[]
[null,"Example 5:"]
[null,"During the financial crisis of 2008, of the ten biggest banks, only three increase lending after they were given TARP funds of about 2 Billion dolars were given out."]
[null,{"$f":"\"If you took at random sample of \"&G119&\" of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, 3?\"","v":"If you took at random sample of 4 of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, 3?"}]
[]
[null,"Experiment = Asking 3 banks out of 10 without replacement, if they increased lending"]
[null,"Success = Bank increase lending"]
[null,"Discrete Variable = X = # of banks that increased lending"]
[]
[null,"Experiment variables:",null,null,null,null,null,null,null,"X","P(X)"]
[null,"Population size = number_pop =",null,null,null,null,10,null,null,{"$f":"_xlfn.SEQUENCE(G119+1,,0)","v":0},{"$f":"_xlfn.HYPGEOM.DIST(_xlfn.ANCHORARRAY(J117),G119,G118,G117,0)","v":0.1666666666666666},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(K117),\"\")","v":"=HYPGEOM.DIST(J117#,G119,G118,G117,0)"}]
[null,"Successes in population = population_s =",null,null,null,null,3,null,null,1,0.49999999999999994]
[null,"n = Fixed number of trials = number_sample =",null,null,null,null,4,null,null,2,0.30000000000000004]
[null,"X1 = counts successes in sample =  sample_s =",null,null,null,null,1,null,null,3,3.3333333333333291E-2]
[null,"X2 = counts successes in sample =  sample_s =",null,null,null,null,3,null,null,4,0]
[]
[null,"Goals:"]
[null,null,"Sample Points for 1 in 4 =",null,null,null,{"$f":"COMBIN(G119,G121)","v":4},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G124:G128),\"\")","v":"=COMBIN(G119,G121)"}]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7*G124","v":0.5},null,"=3/10*(9-2)/9*(8-2)/8*(7-2)/7*G124"]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"SUM(G131:G134)","v":0.49999999999999994},null,"=SUM(G131:G134)"]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(G120,G119,G118,G117,0)","v":0.49999999999999994},null,"=HYPGEOM.DIST(G120,G119,G118,G117,0)"]
[null,null,"P(3 of 4 banks increased lending)",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(G121,G119,G118,G117,0)","v":3.3333333333333291E-2},null,"=HYPGEOM.DIST(G121,G119,G118,G117,0)"]
[]
[null,"Sample Point","Step 1","Step 2","Step 3","Step 4","Prob."]
[null,1,"Lend","Not Lend","Not Lend","Not Lend",{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7","v":0.125},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G131:G134),\"\")","v":"=3/10*(9-2)/9*(8-2)/8*(7-2)/7"}]
[null,2,"Not Lend","Lend","Not Lend","Not Lend",{"$f":"7/10*3/9*(8-2)/8*(7-2)/7","v":0.12499999999999997},null,"=7/10*3/9*(8-2)/8*(7-2)/7"]
[null,3,"Not Lend","Not Lend","Lend","Not Lend",{"$f":"7/10*(7-1)/9*3/8*(7-2)/7","v":0.12499999999999997},null,"=7/10*(7-1)/9*3/8*(7-2)/7"]
[null,4,"Not Lend","Not Lend","Not Lend","Lend",{"$f":"7/10*(7-1)/9*(7-2)/8*3/7","v":0.12499999999999999},null,"=7/10*(7-1)/9*(7-2)/8*3/7"]

{"sheet":"Topics","index":11,"n_rows":17,"n_cols":3,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Chapter 5"]
[]
[null,"Discrete Probability Distributions"]
[]
[]
[null,"Video 23","Discrete Probability Distributions: Terms and Definitions"]
[null,"Video 24","Build Discrete Probability Distributions with Worksheet Formulas"]
[null,"Video 25","Import Excel data: Build PivotTable Discrete Probability Distribution"]
[null,"Video 26","Accounting & Finance Discrete Probability Distribution Examples"]
[null,"Video 27","Binomial Probability Distributions. BINOM.DIST.RANGE Function & Chart"]
[null,"Video 28","Poisson Distribution and POISSON.DIST Function"]
[null,"Video 29","Hypergeometric Distribution and HYPGEOM.DIST Function"]
[]
[]
[null,"Excel Statistical Analysis 27: Binomial Probability Distributions. BINOM.DIST.RANGE Function & Chart"]
[null,{"$f":"LEN(B16)","v":100}]

{"sheet":"PD(1)","index":12,"n_rows":31,"n_cols":7,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Experiment of tossing coin three times"]
["Steps in Experiment",3]
["Outcomes Step 1",2]
["Outcomes Step 2",2]
["Outcomes Step 3",2,null,null,null,"Success ="]
["Total Experimental Outcomes",{"$f":"PRODUCT(B3:B5)","v":8},"(Sample Points)",null,null,"Tails"]
["P(for each) =",{"$f":"1/B6","v":0.125},"Classical",null,null,{"$f":"\"Notation for \"&F6&\" is \"&LEFT(F6,1)","v":"Notation for Tails is T"}]
[null,null,null,null,null,{"$f":"LEFT(F6,1)","v":"T"}]
["# SP","Toss 1","Toss 2","Toss 3","Sample Space","Probability of Sample Point","# of heads for sample points"]
[1,"H","H","H",{"$f":"\"(\"&B10:B17&\", \"&C10:C17&\", \"&D10:D17&\")\"","v":"(H, H, H)"},{"$f":"_xlfn.SEQUENCE(B6,,B7,0)","v":0.125},{"$f":"COUNTIF(B10:D10,$F$8)","v":0}]
[2,"T","H","H","(T, H, H)",0.125,1]
[3,"H","T","H","(H, T, H)",0.125,1]
[4,"H","H","T","(H, H, T)",0.125,1]
[5,"T","T","H","(T, T, H)",0.125,2]
[6,"T","H","T","(T, H, T)",0.125,2]
[7,"H","T","T","(H, T, T)",0.125,2]
[8,"T","T","T","(T, T, T)",0.125,3]
[null,null,null,null,null,{"$f":"SUM(F10:F17)","v":1}]
["x = Discrete Random Variable =",{"$f":"\"# of \"&F6&\" in 3 flips\"","v":"# of Tails in 3 flips"}]
[null,null,null,null,"Steps:","#1","Define Random Variable"]
["X","Frequency","P(X) = f(x)",null,null,"#2","Build Frequency Distribution"]
[0,{"$f":"COUNTIF(G10:G17,A22:A25)","v":1},{"$f":"_xlfn.ANCHORARRAY(B22)/B26","v":0.125},null,null,"#3","Calculate Relative Frequency - P(x) = f(x)"]
[1,3,0.375,null,null,"#4","Check Requirement #1: f(x) >= 0"]
[2,3,0.375,null,null,"#5","Check Requirement #2: Σf(x) = 1"]
[3,1,0.125,null,null,"#6","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["Total",{"$f":"SUM(B22:B25)","v":8},{"$f":"SUM(C22:C25)","v":1},null,null,"#7","Make predictions"]
[]
["P(X =1)",{"$f":"C22","v":0.125}]
["P(X > = 2)",{"$f":"SUM(C24:C25)","v":0.5}]
["P(x = 0 or x = 3)",{"$f":"SUM(C22,C25)","v":0.25},{"$f":"C22+C25","v":0.25}]
["P(X not 2)",{"$f":"SUM(C22:C23,C25)","v":0.625},{"$f":"1-C24","v":0.625}]

{"sheet":"PD(2)","index":13,"n_rows":126,"n_cols":14,"rows_kept":126,"cut":false,"hidden":false,"merged":[]}
["Steps to Build Discrete Probability Distribution:"]
["#1","Define Random Variable"]
["#2","Build Frequency Distribution"]
["#3","Calculate Relative Frequency = P(x) = f(x)"]
["#4","Check Requirement #1: f(x) >= 0 , Check Requirement #2: Σf(x) = 1"]
["#5","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["#6","Make predictions"]
[]
["Worksheet formulas have two advantages over PivotTable: 1) Update instantly when source data changes and 2) You can select part of a report or the whole report and make a chart."]
[]
["Isaac's Italian Restaurant has 4 banquet rooms.",null,null,null,null,null,null,null,null,null,null,null,"Chart Title:","Isaac's Italian Restaurant Discrete Prob. Distribution"]
["Isaac collected the below data over last 6 months.",null,null,"Define Variable:","X = Random Discrete Variable = Number of Rooms Used for the Day"]
["They will get more data later.",null,null,"Number of Rooms",4]
[]
["Date","RoomsUsed",null,"X = # Rooms Used","Frequency","P(X)",null,"Req. 1",null,"X -E(X)","(X - E(X))^2","(X - E(X))^2 * P(X)"]
["2023-01-07",1]
["2023-01-08",2]
[{"$f":"A16+7","v":"2023-01-14"},4]
[{"$f":"A17+7","v":"2023-01-15"},3]
["2023-01-21",3]
["2023-01-22",2,null,"Total",null,null,null,"<Req. 2"]
["2023-01-28",2]
["2023-01-29",2,null,null,null,null,null,null,null,null,"s^2"]
["2023-02-04",4,null,"Mean =  E(x) = µ",null,null,null,null,null,null,"s"]
["2023-02-05",1,null,"Mean"]
["2023-02-11",2,null,"SD = s",null,null,null,null,null,"Sum of Actual Deviations"]
["2023-02-12",2,null,"Population SD"]
["2023-02-18",2]
["2023-02-19",1,null,"P(X <=1)",null,null,null,null,"Some conclusions:"]
["2023-02-25",1,null,"P(X = 2 OR X = 3)",null,null,null,null,"People like the banquet rooms"]
["2023-02-26",2,null,"P(X >0)",null,null,null,null,"Maybe we don't need 4 rooms"]
["2023-03-04",2,null,null,null,null,null,null,"Staffing should anticipate 1-3 rooms being used"]
["2023-03-05",2,null,null,null,null,null,null,"42% of the days 2 rooms are used"]
["2023-03-11",4]
["2023-03-12",2]
["2023-03-18",3]
["2023-03-19",2]
["2023-03-25",3]
["2023-03-26",3]
["2023-04-01",2]
["2023-04-02",2]
["2023-04-08",2]
["2023-04-09",2]
["2023-04-15",3]
["2023-04-16",3]
["2023-04-22",1]
["2023-04-23",1]
["2023-04-29",3]
["2023-04-30",3]
["2023-05-06",1]
["2023-05-07",3]
["2023-05-13",2]
["2023-05-14",3]
["2023-05-20",1]
["2023-05-21",1]
["2023-05-27",2]
["2023-05-28",1]
["2023-06-03",1]
["2023-06-04",4]
["2023-06-10",3]
["2023-06-11",1]
["2023-06-17",3]
["2023-06-18",2]
["2023-06-24",2]
["2023-06-25",2]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,"New Data:"]
[]
[null,null,null,"2023-07-01",2]
[null,null,null,"2023-07-02",3]
[null,null,null,"2023-07-08",3]
[null,null,null,"2023-07-09",2]
[null,null,null,"2023-07-15",2]
[null,null,null,"2023-07-16",2]
[null,null,null,"2023-07-22",1]
[null,null,null,"2023-07-23",2]
[null,null,null,"2023-07-29",2]
[null,null,null,"2023-07-30",3]
[null,null,null,"2023-08-05",0]
[null,null,null,"2023-08-06",3]
[null,null,null,"2023-08-12",4]
[null,null,null,"2023-08-13",3]
[null,null,null,"2023-08-19",1]
[null,null,null,"2023-08-20",2]
[null,null,null,"2023-08-26",2]
[null,null,null,"2023-08-27",1]
[null,null,null,"2023-09-02",2]
[null,null,null,"2023-09-03",3]
[null,null,null,"2023-09-09",2]
[null,null,null,"2023-09-10",2]
[null,null,null,"2023-09-16",3]
[null,null,null,"2023-09-17",3]
[null,null,null,"2023-09-23",1]
[null,null,null,"2023-09-24",1]
[null,null,null,"2023-09-30",2]
[null,null,null,"2023-10-01",1]
[null,null,null,"2023-10-07",3]
[null,null,null,"2023-10-08",3]
[null,null,null,"2023-10-14",2]
[null,null,null,"2023-10-15",2]
[null,null,null,"2023-10-21",2]
[null,null,null,"2023-10-22",2]
[null,null,null,"2023-10-28",1]
[null,null,null,"2023-10-29",2]
[null,null,null,"2023-11-04",4]
[null,null,null,"2023-11-05",0]
[null,null,null,"2023-11-11",4]
[null,null,null,"2023-11-12",2]
[null,null,null,"2023-11-18",1]
[null,null,null,"2023-11-19",3]
[null,null,null,"2023-11-25",4]
[null,null,null,"2023-11-26",3]
[null,null,null,"2023-12-02",3]
[null,null,null,"2023-12-03",2]
[null,null,null,"2023-12-09",1]
[null,null,null,"2023-12-10",3]
[null,null,null,"2023-12-16",2]
[null,null,null,"2023-12-17",2]

{"sheet":"PD(2an)","index":14,"n_rows":126,"n_cols":14,"rows_kept":126,"cut":false,"hidden":false,"merged":[]}
["Steps to Build Discrete Probability Distribution:"]
["#1","Define Random Variable"]
["#2","Build Frequency Distribution"]
["#3","Calculate Relative Frequency = P(x) = f(x)"]
["#4","Check Requirement #1: f(x) >= 0 , Check Requirement #2: Σf(x) = 1"]
["#5","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["#6","Make predictions"]
[]
["Worksheet formulas have two advantages over PivotTable: 1) Update instantly when source data changes and 2) You can select part of a report or the whole report and make a chart."]
[]
["Isaac's Italian Restaurant has 4 banquet rooms.",null,null,null,null,null,null,null,null,null,null,null,"Chart Title:","Isaac's Italian Restaurant Discrete Prob. Distribution"]
["Isaac collected the below data over last 6 months.",null,null,"Define Variable:","X = Random Discrete Variable = Number of Rooms Used for the Day"]
["They will get more data later.",null,null,"Number of Rooms",4]
[]
["Date","RoomsUsed",null,"X = # Rooms Used","Frequency","P(X)",null,"Req. 1",null,"X -E(X)","(X - E(X))^2","(X - E(X))^2 * P(X)",null,"Formulas Used:"]
["2023-01-07",1,null,{"$f":"_xlfn.SEQUENCE(E13+1,,0)","v":0},{"$f":"COUNTIFS(fRoomsAnswer[RoomsUsed],_xlfn.ANCHORARRAY(D16))","v":2},{"$f":"_xlfn.ANCHORARRAY(E16)/E21","v":0.02},null,{"$f":"_xlfn.ANCHORARRAY(F16)>=0","v":true},null,{"$f":"_xlfn.ANCHORARRAY(D16)-E24","v":-2.1800000000000002},{"$f":"_xlfn.ANCHORARRAY(J16)^2","v":4.7524000000000006},{"$f":"_xlfn.ANCHORARRAY(F16)*_xlfn.ANCHORARRAY(K16)","v":9.5048000000000021E-2},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(D16),COLUMN(D16),4)&\": \"&_xlfn.FORMULATEXT(D16),\"\")","v":"D16: =SEQUENCE(E13+1,,0)"}]
["2023-01-08",2,null,1,21,0.21,null,true,null,-1.1800000000000002,1.3924000000000003,0.29240400000000005,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E16),COLUMN(E16),4)&\": \"&_xlfn.FORMULATEXT(E16),\"\")","v":"E16: =COUNTIFS(fRoomsAnswer[RoomsUsed],D16#)"}]
[{"$f":"A16+7","v":"2023-01-14"},4,null,2,42,0.42,null,true,null,-0.18000000000000016,3.2400000000000061E-2,1.3608000000000025E-2,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F16),COLUMN(F16),4)&\": \"&_xlfn.FORMULATEXT(F16),\"\")","v":"F16: =E16#/E21"}]
[{"$f":"A17+7","v":"2023-01-15"},3,null,3,27,0.27,null,true,null,0.81999999999999984,0.67239999999999978,0.18154799999999996]
["2023-01-21",3,null,4,8,0.08,null,true,null,1.8199999999999998,3.3123999999999993,0.26499199999999995,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E21),COLUMN(E21),4)&\": \"&_xlfn.FORMULATEXT(E21),\"\")","v":"E21: =SUM(E16#)"}]
["2023-01-22",2,null,"Total",{"$f":"SUM(_xlfn.ANCHORARRAY(E16))","v":100},{"$f":"SUM(_xlfn.ANCHORARRAY(F16))","v":0.99999999999999989},null,"<Req. 2",null,{"$f":"SUM(_xlfn.ANCHORARRAY(J16))","v":-0.9000000000000008},null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F21),COLUMN(F21),4)&\": \"&_xlfn.FORMULATEXT(F21),\"\")","v":"F21: =SUM(F16#)"}]
["2023-01-28",2,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(H16),COLUMN(H16),4)&\": \"&_xlfn.FORMULATEXT(H16),\"\")","v":"H16: =F16#>=0"}]
["2023-01-29",2,null,null,null,null,null,null,null,null,"s^2",{"$f":"SUM(_xlfn.ANCHORARRAY(L16))","v":0.84759999999999991}]
["2023-02-04",4,null,"Mean =  E(x) = µ",{"$f":"SUMPRODUCT(_xlfn.ANCHORARRAY(D16),_xlfn.ANCHORARRAY(F16))","v":2.1800000000000002},null,null,null,null,null,"s",{"$f":"SQRT(L23)","v":0.92065194291871233},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(J16),COLUMN(J16),4)&\": \"&_xlfn.FORMULATEXT(J16),\"\")","v":"J16: =D16#-E24"}]
["2023-02-05",1,null,"Mean",{"$f":"AVERAGE(fRoomsAnswer[RoomsUsed])","v":2.1800000000000002},null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(K16),COLUMN(K16),4)&\": \"&_xlfn.FORMULATEXT(K16),\"\")","v":"K16: =J16#^2"}]
["2023-02-11",2,null,"SD = s",{"$f":"SQRT(SUM((_xlfn.ANCHORARRAY(D16)-E24)^2*_xlfn.ANCHORARRAY(F16)))","v":0.92065194291871233},null,null,null,null,"Sum of Actual Deviations",null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(L16),COLUMN(L16),4)&\": \"&_xlfn.FORMULATEXT(L16),\"\")","v":"L16: =F16#*K16#"}]
["2023-02-12",2,null,"Population SD",{"$f":"_xlfn.STDEV.P(fRoomsAnswer[RoomsUsed])","v":0.92065194291871233},null,null,null,null,{"$f":"SUM(fRoomsAnswer[RoomsUsed]-E24)","v":-1.5987211554602254E-14}]
["2023-02-18",2,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E24),COLUMN(E24),4)&\": \"&_xlfn.FORMULATEXT(E24),\"\")","v":"E24: =SUMPRODUCT(D16#,F16#)"}]
["2023-02-19",1,null,"P(X <=1)",{"$f":"SUM(F16:F17)","v":0.22999999999999998},null,null,null,"Some conclusions:",null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E25),COLUMN(E25),4)&\": \"&_xlfn.FORMULATEXT(E25),\"\")","v":"E25: =AVERAGE(fRoomsAnswer[RoomsUsed])"}]
["2023-02-25",1,null,"P(X = 2 OR X = 3)",{"$f":"SUM(F18:F19)","v":0.69},null,null,null,"People like the banquet rooms",null,null,null,null,"E26: =SQRT(SUM((D16#-E24)^2*F16#))"]
["2023-02-26",2,null,"P(X >0)",{"$f":"SUM(F17:F20)","v":0.98},null,null,null,"Maybe we don't need 4 rooms",null,null,null,null,"E27: =STDEV.P(fRoomsAnswer[RoomsUsed])"]
["2023-03-04",2,null,null,null,null,null,null,"Staffing should anticipate 1-3 rooms being used",null,null,null,null,""]
["2023-03-05",2,null,null,null,null,null,null,"42% of the days 2 rooms are used",null,null,null,null,"E29: =SUM(F16:F17)"]
["2023-03-11",4,null,null,null,null,null,null,null,null,null,null,null,"E30: =SUM(F18:F19)"]
["2023-03-12",2,null,null,null,null,null,null,null,null,null,null,null,"E31: =SUM(F17:F20)"]
["2023-03-18",3,null,null,null,null,null,null,null,null,null,null,null,""]
["2023-03-19",2]
["2023-03-25",3]
["2023-03-26",3]
["2023-04-01",2]
["2023-04-02",2]
["2023-04-08",2]
["2023-04-09",2]
["2023-04-15",3]
["2023-04-16",3]
["2023-04-22",1]
["2023-04-23",1]
["2023-04-29",3]
["2023-04-30",3]
["2023-05-06",1]
["2023-05-07",3]
["2023-05-13",2]
["2023-05-14",3]
["2023-05-20",1]
["2023-05-21",1]
["2023-05-27",2]
["2023-05-28",1]
["2023-06-03",1]
["2023-06-04",4]
["2023-06-10",3]
["2023-06-11",1]
["2023-06-17",3]
["2023-06-18",2]
["2023-06-24",2]
["2023-06-25",2]
["2023-07-01",2]
["2023-07-02",3]
["2023-07-08",3]
["2023-07-09",2]
["2023-07-15",2]
["2023-07-16",2]
["2023-07-22",1]
["2023-07-23",2]
["2023-07-29",2]
["2023-07-30",3,null,"New Data:"]
["2023-08-05",0]
["2023-08-06",3,null,"2023-07-01",2]
["2023-08-12",4,null,"2023-07-02",3]
["2023-08-13",3,null,"2023-07-08",3]
["2023-08-19",1,null,"2023-07-09",2]
["2023-08-20",2,null,"2023-07-15",2]
["2023-08-26",2,null,"2023-07-16",2]
["2023-08-27",1,null,"2023-07-22",1]
["2023-09-02",2,null,"2023-07-23",2]
["2023-09-03",3,null,"2023-07-29",2]
["2023-09-09",2,null,"2023-07-30",3]
["2023-09-10",2,null,"2023-08-05",0]
["2023-09-16",3,null,"2023-08-06",3]
["2023-09-17",3,null,"2023-08-12",4]
["2023-09-23",1,null,"2023-08-13",3]
["2023-09-24",1,null,"2023-08-19",1]
["2023-09-30",2,null,"2023-08-20",2]
["2023-10-01",1,null,"2023-08-26",2]
["2023-10-07",3,null,"2023-08-27",1]
["2023-10-08",3,null,"2023-09-02",2]
["2023-10-14",2,null,"2023-09-03",3]
["2023-10-15",2,null,"2023-09-09",2]
["2023-10-21",2,null,"2023-09-10",2]
["2023-10-22",2,null,"2023-09-16",3]
["2023-10-28",1,null,"2023-09-17",3]
["2023-10-29",2,null,"2023-09-23",1]
["2023-11-04",4,null,"2023-09-24",1]
["2023-11-05",0,null,"2023-09-30",2]
["2023-11-11",4,null,"2023-10-01",1]
["2023-11-12",2,null,"2023-10-07",3]
["2023-11-18",1,null,"2023-10-08",3]
["2023-11-19",3,null,"2023-10-14",2]
["2023-11-25",4,null,"2023-10-15",2]
["2023-11-26",3,null,"2023-10-21",2]
["2023-12-02",3,null,"2023-10-22",2]
["2023-12-03",2,null,"2023-10-28",1]
["2023-12-09",1,null,"2023-10-29",2]
["2023-12-10",3,null,"2023-11-04",4]
["2023-12-16",2,null,"2023-11-05",0]
["2023-12-17",2,null,"2023-11-11",4]
[null,null,null,"2023-11-12",2]
[null,null,null,"2023-11-18",1]
[null,null,null,"2023-11-19",3]
[null,null,null,"2023-11-25",4]
[null,null,null,"2023-11-26",3]
[null,null,null,"2023-12-02",3]
[null,null,null,"2023-12-03",2]
[null,null,null,"2023-12-09",1]
[null,null,null,"2023-12-10",3]
[null,null,null,"2023-12-16",2]
[null,null,null,"2023-12-17",2]

{"sheet":"PD(3)","index":15,"n_rows":1319,"n_cols":11,"rows_kept":1319,"cut":false,"hidden":false,"merged":[]}
["Steps to Build Discrete Probability Distribution:"]
["#1","Define Random Variable"]
["#2","Build Frequency Distribution"]
["#3","Calculate Relative Frequency = P(x) = f(x)"]
["#4","Check Requirement #1: f(x) >= 0 , Check Requirement #2: Σf(x) = 1"]
["#5","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["#6","Make predictions"]
[]
["Data collected: Number of Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period."]
["Discrete Variable =","X = Number of Arrivals in 1 min period during Sat. noon lunch rush (noon to 1 PM)"]
[]
[null,null,"Max No. Arrivals",null,null,null,null,null,"Chart Title:","Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch arrivals during a 1-minute period."]
[]
["X = Arrivals During 1 min",null,"X = Arrivals During 1 min","Frequency","P(X)",null,"Req. 1"]
[0,null,null,null,null,null,null,null,"Mean",null,{"$f":"AVERAGE(A15:A1319)","v":3.8796934865900381}]
[0,null,null,null,null,null,null,null,"SD",null,{"$f":"SQRT(_xlfn.VAR.P(A15:A1319))","v":1.9369589225730506}]
[0]
[0,null,null,null,null,null,null,null,"P(X <=2)"]
[0,null,null,null,null,null,null,null,"P(X = 3 OR X = 4 OR x = 5)"]
[0,null,null,null,null,null,null,null,"P(X > 0)"]
[0]
[0,null,null,null,null,null,null,null,"Some conclusions:"]
[0,null,null,null,null,null,null,null,"40% of the time you would expect 3 or 4 people showing up for any given minute period."]
[0,null,null,null,null,null,null,null,"50% of the time you would expect 3-5 people showing up for any given minute period."]
[0,null,null,null,null,null,null,null,"About 2% of the time no customers show up during a given lunch hour minute"]
[0]
[0]
[0]
[0]
[0,null,"Total",null,null,null,"<Req. 2"]
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{"sheet":"PD(3an)","index":16,"n_rows":1319,"n_cols":36,"rows_kept":1319,"cut":false,"hidden":false,"merged":[]}
["Steps to Build Discrete Probability Distribution:"]
["#1","Define Random Variable"]
["#2","Build Frequency Distribution"]
["#3","Calculate Relative Frequency = P(x) = f(x)"]
["#4","Check Requirement #1: f(x) >= 0 , Check Requirement #2: Σf(x) = 1"]
["#5","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["#6","Make predictions"]
[]
["Data collected: Number of Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period."]
["Discrete Variable =","X = Number of Arrivals in 1 min period during Sat. noon lunch rush (noon to 1 PM)"]
[]
[null,null,"Max No. Arrivals",{"$f":"MAX(A15:A1319)","v":14},null,null,null,null,"Chart Title:","Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch arrivals during a 1-minute period."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Comment from below Video #24 from ExcelLambda:"]
["X = Arrivals During 1 min",null,"X = Arrivals During 1 min","Frequency","P(X)",null,"Req. 1"]
[0,null,{"$f":"_xlfn.SEQUENCE(D12+1,,0)","v":0},{"$f":"COUNTIFS(A15:A1319,_xlfn.ANCHORARRAY(C15))","v":28},{"$f":"_xlfn.ANCHORARRAY(D15)/D30","v":2.1455938697318006E-2},null,{"$f":"_xlfn.ANCHORARRAY(E15)>=0","v":true},null,"Mean",{"$f":"SUMPRODUCT(_xlfn.ANCHORARRAY(C15),_xlfn.ANCHORARRAY(E15))","v":3.8796934865900377},{"$f":"AVERAGE(A15:A1319)","v":3.8796934865900381}]
[0,null,1,102,7.8160919540229884E-2,null,true,null,"SD",{"$f":"SQRT(SUM((_xlfn.ANCHORARRAY(C15)-J15)^2*_xlfn.ANCHORARRAY(E15)))","v":1.9369589225730508},{"$f":"SQRT(_xlfn.VAR.P(A15:A1319))","v":1.9369589225730506}]
[0,null,2,191,0.14636015325670498,null,true]
[0,null,3,263,0.20153256704980843,null,true,null,"P(X <=2)",{"$f":"SUM(E15:E17)","v":0.24597701149425288}]
[0,null,4,266,0.20383141762452106,null,true,null,"P(X = 3 OR X = 4 OR x = 5)",{"$f":"SUM(E18:E20)","v":0.56168582375478926}]
[0,null,5,204,0.15632183908045977,null,true,null,"P(X > 0)",{"$f":"1-E15","v":0.97854406130268201}]
[0,null,6,136,0.10421455938697317,null,true]
[0,null,7,70,5.3639846743295021E-2,null,true,null,"Some conclusions:",null,null,null,null,null,null,null,null,"Formulas Used:"]
[0,null,8,22,1.6858237547892719E-2,null,true,null,"40% of the time you would expect 3 or 4 people showing up for any given minute period.",null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(D12),COLUMN(D12),4)&\": \"&_xlfn.FORMULATEXT(D12),\"\")","v":"D12: =MAX(A15:A1319)"}]
[0,null,9,14,1.0727969348659003E-2,null,true,null,"50% of the time you would expect 3-5 people showing up for any given minute period."]
[0,null,10,5,3.8314176245210726E-3,null,true,null,"About 2% of the time no customers show up during a given lunch hour minute",null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C15),COLUMN(C15),4)&\": \"&_xlfn.FORMULATEXT(C15),\"\")","v":"C15: =SEQUENCE(D12+1,,0)"}]
[0,null,11,2,1.5325670498084292E-3,null,true,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(D15),COLUMN(D15),4)&\": \"&_xlfn.FORMULATEXT(D15),\"\")","v":"D15: =COUNTIFS(A15:A1319,C15#)"}]
[0,null,12,1,7.6628352490421458E-4,null,true,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E15),COLUMN(E15),4)&\": \"&_xlfn.FORMULATEXT(E15),\"\")","v":"E15: =D15#/D30"}]
[0,null,13,0,0,null,true]
[0,null,14,1,7.6628352490421458E-4,null,true,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(D30),COLUMN(D30),4)&\": \"&_xlfn.FORMULATEXT(D30),\"\")","v":"D30: =SUM(D15#)"}]
[0,null,"Total",{"$f":"SUM(_xlfn.ANCHORARRAY(D15))","v":1305},{"$f":"SUM(_xlfn.ANCHORARRAY(E15))","v":1},null,"<Req. 2",null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E30),COLUMN(E30),4)&\": \"&_xlfn.FORMULATEXT(E30),\"\")","v":"E30: =SUM(E15#)"}]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(G15),COLUMN(G15),4)&\": \"&_xlfn.FORMULATEXT(G15),\"\")","v":"G15: =E15#>=0"}]
[0]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(J15),COLUMN(J15),4)&\": \"&_xlfn.FORMULATEXT(J15),\"\")","v":"J15: =SUMPRODUCT(C15#,E15#)"}]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(J16),COLUMN(J16),4)&\": \"&_xlfn.FORMULATEXT(J16),\"\")","v":"J16: =SQRT(SUM((C15#-J15)^2*E15#))"}]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,{"$f":"DSCFRQ(A15:A1319,C14:E14)","v":"X = Arrivals During 1 min"},"Frequency","P(X)",null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(AB35),COLUMN(AB35),4)&\": \"&_xlfn.FORMULATEXT(AB35),\"\")","v":"AB35: =DSCFRQ(A15:A1319,C14:E14)"}]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"J18: =SUM(E15:E17)",null,null,null,null,null,null,null,null,null,0,28,2.1455938697318006E-2]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"J19: =SUM(E18:E20)",null,null,null,null,null,null,null,null,null,1,102,7.8160919540229884E-2,null,{"$f":"_xlfn.LAMBDA(_xlpm.a,_xlop.h,_xlfn.LET(_xlpm.r,ROWS(_xlpm.a),_xlpm.u,_xlfn._xlws.SORT(_xlfn.UNIQUE(_xlpm.a)),_xlpm.w,ROWS(_xlpm.u),_xlpm.f,_xlfn.MAP(_xlpm.u,_xlfn.LAMBDA(_xlpm.x,SUM(--(_xlpm.x=_xlpm.a)))),_xlpm.p,_xlpm.f/_xlpm.r,_xlpm.b,CHOOSE({1,2,3},_xlpm.u,_xlpm.f,_xlpm.p),_xlpm.tr,CHOOSE({1,2,3},_xlpm.h,\"Frequency\",\"P(X)\"),_xlpm.br,CHOOSE({1,2,3},\"Total\",_xlpm.r,1),_xlpm.s,_xlfn.SEQUENCE(_xlpm.w+2)-1,_xlfn.SWITCH(_xlpm.s,0,_xlpm.tr,_xlpm.w+1,_xlpm.br,INDEX(_xlpm.b,_xlpm.s,{1,2,3}))))(A15:A1319,C14:E14)","v":"X = Arrivals During 1 min"},"Frequency","P(X)",null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(AF37),COLUMN(AF37),4)&\": \"&_xlfn.FORMULATEXT(AF37),\"\")","v":"AF37: =LAMBDA(a,[h],LET(r,ROWS(a),u,SORT(UNIQUE(a)),w,ROWS(u),f,MAP(u,LAMBDA(x,SUM(--(x=a)))),p,f/r,b,CHOOSE({1,2,3},u,f,p),tr,CHOOSE({1,2,3},h,\"Frequency\",\"P(X)\"),br,CHOOSE({1,2,3},\"Total\",r,1),s,SEQUENCE(w+2)-1,SWITCH(s,0,tr,w+1,br,INDEX(b,s,{1,2,3}))))(A15:A1319,C14:E14)"}]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"J20: =1-E15",null,null,null,null,null,null,null,null,null,2,191,0.14636015325670498,null,0,28,2.1455938697318006E-2]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,263,0.20153256704980843,null,1,102,7.8160919540229884E-2]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4,266,0.20383141762452106,null,2,191,0.14636015325670498]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5,204,0.15632183908045977,null,3,263,0.20153256704980843]
[0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,136,0.10421455938697317,null,4,266,0.20383141762452106]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7,70,5.3639846743295021E-2,null,5,204,0.15632183908045977]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,22,1.6858237547892719E-2,null,6,136,0.10421455938697317]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9,14,1.0727969348659003E-2,null,7,70,5.3639846743295021E-2]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10,5,3.8314176245210726E-3,null,8,22,1.6858237547892719E-2]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,11,2,1.5325670498084292E-3,null,9,14,1.0727969348659003E-2]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12,1,7.6628352490421458E-4,null,10,5,3.8314176245210726E-3]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,14,1,7.6628352490421458E-4,null,11,2,1.5325670498084292E-3]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Total",1305,1,null,12,1,7.6628352490421458E-4]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,14,1,7.6628352490421458E-4]
[1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Total",1305,1]
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{"sheet":"PQ Notes","index":17,"n_rows":27,"n_cols":3,"rows_kept":27,"cut":false,"hidden":false,"merged":[[3,1,3,12],[2,1,2,12],[14,1,14,12],[26,1,26,12]]}
[]
[null,"Power Query to import data:"]
[null,"1) When you import data from a CSV file, the file usually has just one object: a table. You can use the From Text/CSV button in the Get & Transform group in the Data tab in the Excel Ribbon to import CSV data."]
[null,"2) When you import data from an Excel file, the file can have more than one object. An Excel file can have objects such as Worksheets, Excel Tables, or Defined Names. Therefore, when you use Power Query to import a table of data from an Excel file, during the import process you must select the object that you want to import. In this video, we will select the Worksheet object named \"MonclaireGolf\"."]
[null,"To import a table of data from a single Excel file, you can follow these steps:"]
[null,null,"1) Get & Transform group in the Data tab in the Excel Ribbon"]
[null,null,"2) Click Get Data dropdown arrow"]
[null,null,"3) From the dropdown menu, hover over \"From File\""]
[null,null,"4) Click on \"From Excel Workbook\""]
[null,null,"5) Select file from Import Data File dialog box"]
[null,null,"6) In the Navigator dialog box, on the left side, select the object that has the data table that you want to import"]
[null,null,"7) Click the \"Transform Data\" button to bring the object into the Power Query Editor"]
[null,null,"8) Make transformations you want in Power Query Editor, then Close and Load your table."]
[null,"Power Query Import Data dialog box to import table directly to PivotTable Cache:"]
[null,"To import a table of data directly to the PivotTable Cache: Select the \"PivotTable Report\" dialog button in the Import Data dialog box, as shown here:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"If you do not need the table of data in the worksheet, loading directly to the PivotTable Cache, avoids loading the table to two locations (worksheet and PivotTable Cache). This can reduce file size and avoid have to refresh both the query and the PivotTable report when source data changes."]

{"sheet":"PD(4)","index":18,"n_rows":22,"n_cols":12,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
[]
["1)","Download the data file \"MonclaireGolf.xlsx\" from this link:",null,null,null,null,null,null,null,null,"https://people.highline.edu/mgirvin/AllClasses/B210/Ch05/Ch05.htm"]
["2)","Save the the data file \"MonclaireGolf.xlsx\" to the folder you created in Video #1 (folder with your name)."]
["3)","Using the Get Data, From File, From Excel Workbook feature in the Get & Transform Data group in the Data tab in the Excel ribbon,"]
[null,"import the data file \"MonclaireGolf.xlsx\" onto this worksheet."]
["4)","Create Discrete Probability Distribution"]
[]
[null,"Summer 2021, Monclaire Gold in Oakland, CA"]
[null,"400 rounds of golf in data set"]
[null,"each number is the score for one player for hole #9"]
[]
[null,"Random Descrete Variable = score on hole #9"]
[null,"Par = 3"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Notation","P(X)"]
[null,null,null,null,null,null,null,null,null,null,"P(<=3)"]
[null,null,null,null,null,null,null,null,null,null,"P(>3)"]
[null,null,null,null,null,null,null,null,null,null,"P(3)"]
[null,null,null,null,null,null,null,null,null,null,"E(x) = μ = Mean"]
[null,null,null,null,null,null,null,null,null,null,"Var(X) = σ^2 ="]
[null,null,null,null,null,null,null,null,null,null,"SD = σ ="]

{"sheet":"PD(4an)","index":19,"n_rows":23,"n_cols":14,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
[]
["1)","Download the data file \"MonclaireGolf.xlsx\" from this link:",null,null,null,null,null,null,null,null,"https://people.highline.edu/mgirvin/AllClasses/B210/Ch05/Ch05.htm"]
["2)","Save the the data file \"MonclaireGolf.xlsx\" to the folder you created in Video #1 (folder with your name)."]
["3)","Using the Get Data, From File, From Excel Workbook feature in the Get & Transform Data group in the Data tab in the Excel ribbon,"]
[null,"import the data file \"MonclaireGolf.xlsx\" onto this worksheet."]
["4)","Create Discrete Probability Distribution"]
[]
[null,"Summer 2021, Monclaire Gold in Oakland, CA"]
[null,"400 rounds of golf in data set"]
[null,"each number is the score for one player for hole #9"]
[]
[null,"Random Descrete Variable = score on hole #9"]
[null,"Par = 3"]
[]
[]
[null,"Hole 9 Score (X)","Frequency","P(X)",null,null,null,null,null,null,"Notation","P(X)",null,"Formulas Used:"]
[null,2,4,0.01,null,null,null,null,null,null,"P(<=3)",{"$f":"SUM(D17:D18)","v":0.14750000000000002},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(L17),COLUMN(L17),4)&\": \"&_xlfn.FORMULATEXT(L17),\"\")","v":"L17: =SUM(D17:D18)"}]
[null,3,55,0.13750000000000001,null,null,null,null,null,null,"P(>3)",{"$f":"SUM(D19:D22)","v":0.85250000000000015},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(L18),COLUMN(L18),4)&\": \"&_xlfn.FORMULATEXT(L18),\"\")","v":"L18: =SUM(D19:D22)"}]
[null,4,185,0.46250000000000002,null,null,null,null,null,null,"P(3)",{"$f":"D18","v":0.13750000000000001},null,"L19: =D18"]
[null,5,130,0.32500000000000001,null,null,null,null,null,null,"E(x) = μ = Mean",{"$f":"SUMPRODUCT(B17:B22,D17:D22)","v":4.3075000000000001},null,"L20: =SUMPRODUCT(B17:B22,D17:D22)"]
[null,6,22,5.5E-2,null,null,null,null,null,null,"Var(X) = σ^2 =",{"$f":"SUM((B17:B22-L20)^2*D17:D22)","v":0.7179437500000001},null,"L21: =SUM((B17:B22-L20)^2*D17:D22)"]
[null,7,4,0.01,null,null,null,null,null,null,"SD = σ =",{"$f":"SQRT(L21)","v":0.8473156141603907},null,"L22: =SQRT(L21)"]
[null,"Grand Total",400,1]

{"sheet":"EVSD(1)","index":20,"n_rows":126,"n_cols":6,"rows_kept":126,"cut":false,"hidden":false,"merged":[]}
["Unit Demand = x","Prob = f(x)"]
[500,0.1]
[600,0.15]
[700,0.15]
[800,0.2]
[900,0.2]
[1000,0.15]
[1100,0.05]
[null,{"$f":"SUM(B2:B8)","v":1}]
[]
["Mean = Expected Value",null," = monthly order quantity"]
["SD"]
[]
["Price per unit",125]
["Cost per unit",60]
["Units sold for cash",500]
["Cash IN"]
["Cash OUT"]
["Cash Flow Implication",null,null,"NOT Accrual Accounting Profit"]
[]
[]
[]
[null,"All Values",null,null,"Mean = Expected Value",{"$f":"AVERAGE(B24:B123)","v":790}]
[null,500,null,null,"SD",{"$f":"_xlfn.STDEV.P(B24:B123)","v":170}]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
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[null,1000]
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[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
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[null,1000]
[null,1000]
[null,1000]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
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[]
["VAR.P",{"$f":"_xlfn.VAR.P(B24:B123)","v":28900}]
["STDEV.S",{"$f":"_xlfn.STDEV.P(B24:B123)","v":170}]

{"sheet":"EVSD(1an)","index":21,"n_rows":126,"n_cols":8,"rows_kept":126,"cut":false,"hidden":false,"merged":[]}
["Unit Demand = x","Prob = f(x)"]
[500,0.1]
[600,0.15]
[700,0.15]
[800,0.2]
[900,0.2]
[1000,0.15]
[1100,0.05]
[null,{"$f":"SUM(B2:B8)","v":1},null,null,null,null,null,"Formulas Used:"]
[]
["Mean = Expected Value",{"$f":"SUMPRODUCT(A2:A8,B2:B8)","v":790}," = monthly order quantity",null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B11),COLUMN(B11),4)&\": \"&_xlfn.FORMULATEXT(B11),\"\")","v":"B11: =SUMPRODUCT(A2:A8,B2:B8)"}]
["SD",{"$f":"SQRT(SUMPRODUCT((A2:A8-B11)^2,B2:B8))","v":170},null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B12),COLUMN(B12),4)&\": \"&_xlfn.FORMULATEXT(B12),\"\")","v":"B12: =SQRT(SUMPRODUCT((A2:A8-B11)^2,B2:B8))"}]
[null,null,null,null,null,null,null,""]
["Price per unit",125,null,null,null,null,null,""]
["Cost per unit",60,null,null,null,null,null,""]
["Units sold for cash",500,null,null,null,null,null,""]
["Cash IN",{"$f":"B16*B14","v":62500},null,null,null,null,null,"B17: =B16*B14"]
["Cash OUT",{"$f":"B11*B15","v":47400},null,null,null,null,null,"B18: =B11*B15"]
["Cash Flow Implication",{"$f":"B17-B18","v":15100},null,"NOT Accrual Accounting Profit",null,null,null,"B19: =B17-B18"]
[]
[]
[]
[null,"All Values",null,null,"Mean = Expected Value",{"$f":"AVERAGE(B24:B123)","v":790},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F23),COLUMN(F23),4)&\": \"&_xlfn.FORMULATEXT(F23),\"\")","v":"F23: =AVERAGE(B24:B123)"}]
[null,500,null,null,"SD",{"$f":"_xlfn.STDEV.P(B24:B123)","v":170},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F24),COLUMN(F24),4)&\": \"&_xlfn.FORMULATEXT(F24),\"\")","v":"F24: =STDEV.P(B24:B123)"}]
[null,500]
[null,500]
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[null,900]
[null,900]
[null,900]
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[null,900]
[null,900]
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[null,1000]
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[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
[]
["VAR.P",{"$f":"_xlfn.VAR.P(B24:B123)","v":28900}]
["STDEV.S",{"$f":"_xlfn.STDEV.P(B24:B123)","v":170}]

{"sheet":"EVSD(2)","index":22,"n_rows":8,"n_cols":5,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
["State of Economy","Prob. Of State of Economy","Stock A Return","Stock B Return","Stock C Return"]
["Boom",0.15,0.15,0.25,0.11]
["Normal",{"$f":"1-SUM(B2,B4)","v":0.29999999999999993},7.0000000000000007E-2,0.13,0.1]
["Bust",0.55000000000000004,-0.02,-0.13500000000000001,0.03]
[null,"E(Ri)"]
["Sd = Proxy for Risk","Standard Deviation"]
[null,"CV = SD/Mean"]
[null,"Mean/SD"]

{"sheet":"EVSD(2an)","index":23,"n_rows":8,"n_cols":23,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
["State of Economy","Prob. Of State of Economy","Stock A Return","Stock B Return","Stock C Return",null,null,null,null,null,null,null,null,null,"State of Economy","Prob. Of State of Economy","Stock A Return","Stock B Return","Stock C Return"]
["Boom",0.15,0.15,0.25,0.11,null,null,null,null,null,null,null,null,null,"Boom",0.15,0.15,0.25,0.11]
["Normal",{"$f":"1-SUM(B2,B4)","v":0.29999999999999993},7.0000000000000007E-2,0.13,0.1,null,null,null,null,null,null,null,null,null,"Normal",{"$f":"1-SUM(P2,P4)","v":0.29999999999999993},7.0000000000000007E-2,0.13,0.1]
["Bust",0.55000000000000004,-0.02,-0.13500000000000001,0.03,null,null,null,"Formulas Used:",null,null,null,null,null,"Bust",0.55000000000000004,-0.02,-0.13500000000000001,0.03,null,null,null,"Formulas Used:"]
[null,"E(Ri)",{"$f":"SUMPRODUCT($B$2:$B$4,C2:C4)","v":3.2499999999999994E-2},{"$f":"SUMPRODUCT($B$2:$B$4,D2:D4)","v":2.2499999999999742E-3},6.3E-2,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E5),COLUMN(E5),4)&\": \"&_xlfn.FORMULATEXT(E5),\"\")","v":"E5: =SUMPRODUCT($B$2:$B$4,E2:E4)"},null,null,null,null,null,null,"E(Ri)",{"$f":"_xlfn.BYCOL(Q2:S4,_xlfn.LAMBDA(_xlpm.c,SUM(P2:P4*_xlpm.c)))","v":3.2499999999999994E-2},2.2499999999999742E-3,6.3E-2,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(Q5:Q8),COLUMN(Q5:Q8),4)&\": \"&_xlfn.FORMULATEXT(Q5:Q8),\"\")","v":"Q5: =BYCOL(Q2:S4,LAMBDA(c,SUM(P2:P4*c)))"}]
["Sd = Proxy for Risk","Standard Deviation",{"$f":"SQRT(SUMPRODUCT((C2:C4-C5)^2,$B$2:$B$4))","v":6.3314690238522056E-2},{"$f":"SQRT(SUMPRODUCT((D2:D4-D5)^2,$B$2:$B$4))","v":0.15640871938610074},{"$f":"SQRT(SUMPRODUCT((E2:E4-E5)^2,$B$2:$B$4))","v":3.661966684720111E-2},null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E6),COLUMN(E6),4)&\": \"&_xlfn.FORMULATEXT(E6),\"\")","v":"E6: =SQRT(SUMPRODUCT((E2:E4-E5)^2,$B$2:$B$4))"},null,null,null,null,null,"Sd = Proxy for Risk","Standard Deviation",{"$f":"_xlfn.BYCOL((Q2:S4-_xlfn.ANCHORARRAY(Q5))^2,_xlfn.LAMBDA(_xlpm.c,SQRT(SUM(_xlpm.c*P2:P4))))","v":6.3314690238522056E-2},0.15640871938610074,3.661966684720111E-2,null,null,null,"Q6: =BYCOL((Q2:S4-Q5#)^2,LAMBDA(c,SQRT(SUM(c*P2:P4))))"]
[null,"CV = SD/Mean",{"$f":"C6/C5","v":1.9481443150314481},{"$f":"D6/D5","v":69.514986393823349},0.58126455313017633,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E7),COLUMN(E7),4)&\": \"&_xlfn.FORMULATEXT(E7),\"\")","v":"E7: =E6/E5"},null,null,null,null,null,null,"CV = SD/Mean",{"$f":"_xlfn.ANCHORARRAY(Q6)/_xlfn.ANCHORARRAY(Q5)","v":1.9481443150314481},69.514986393823349,0.58126455313017633,null,null,null,"Q7: =Q6#/Q5#"]
[null,"Mean/SD",{"$f":"C5/C6","v":0.5133089947619498},{"$f":"D5/D6","v":1.438538726505244E-2},1.7203870330899849,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E8),COLUMN(E8),4)&\": \"&_xlfn.FORMULATEXT(E8),\"\")","v":"E8: =E5/E6"},null,null,null,null,null,null,"Mean/SD",{"$f":"_xlfn.ANCHORARRAY(Q5)/_xlfn.ANCHORARRAY(Q6)","v":0.5133089947619498},1.438538726505244E-2,1.7203870330899849,null,null,null,"Q8: =Q5#/Q6#"]

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["pi =",0.2]
["1 - pi =",{"$f":"1-B1","v":0.8}]
["n =",4]
["Fixed # of Trials?","Yes"]
["Each Trial Independent?","Yes"]
["Success is?","Sale","S"]
["Fail is?","No Sale","NS"]
["Success or fail each trial?","Yes"]
["pi the same each Trial?","Yes"]
["Sample Space =",{"$f":"2^B3","v":16}]
[]
[{"$f":"\"Build Discrete Probability Distribution with \"&A3&\" \"&B3&\", \"&A1&\" \"&B1","v":"Build Discrete Probability Distribution with n = 4, pi = 0.2"}]
["Possible Outcomes","Attempted Sale",null,null,null,"# of Sales","Probability associated with each attempt",null,null,null,"Probability of Occurrence Calculation","Probability of Occurrence",null,"# of Sales (Random Variable X)","P(x)","P(x)"]
[null,"1st","2nd","3rd","4th",null,"1st","2nd","3rd","4th"]
[1,"S","S","S","S",{"$f":"COUNTIF(B15:E15,$C$6)","v":4},{"$f":"IF(B15:E15=$C$6,$B$1,$B$2)","v":0.2},0.2,0.2,0.2,{"$f":"G15:G30&\"*\"&H15:H30&\"*\"&I15:I30&\"*\"&J15:J30&\" =\"","v":"0.2*0.2*0.2*0.2 ="},{"$f":"PRODUCT(G15:J15)","v":1.6000000000000005E-3},null,{"$f":"_xlfn.SEQUENCE(B3+1,,0)","v":0},{"$f":"\"P(\"&_xlfn.ANCHORARRAY(N15)&\") =\"","v":"P(0) ="},{"$f":"SUMIF(F15:F30,_xlfn.ANCHORARRAY(N15),L15:L30)","v":0.40960000000000013}]
[2,"S","S","S","NS",3,{"$f":"IF(B16:E16=$C$6,$B$1,$B$2)","v":0.2},0.2,0.2,0.8,"0.2*0.2*0.2*0.8 =",6.400000000000002E-3,null,1,"P(1) =",0.40960000000000013]
[3,"S","S","NS","S",3,{"$f":"IF(B17:E17=$C$6,$B$1,$B$2)","v":0.2},0.2,0.8,0.2,"0.2*0.2*0.8*0.2 =",6.400000000000002E-3,null,2,"P(2) =",0.15360000000000004]
[4,"S","NS","S","S",3,{"$f":"IF(B18:E18=$C$6,$B$1,$B$2)","v":0.2},0.8,0.2,0.2,"0.2*0.8*0.2*0.2 =",6.400000000000002E-3,null,3,"P(3) =",2.5600000000000008E-2]
[5,"NS","S","S","S",3,{"$f":"IF(B19:E19=$C$6,$B$1,$B$2)","v":0.8},0.2,0.2,0.2,"0.8*0.2*0.2*0.2 =",6.400000000000002E-3,null,4,"P(4) =",1.6000000000000005E-3]
[6,"S","S","NS","NS",2,{"$f":"IF(B20:E20=$C$6,$B$1,$B$2)","v":0.2},0.2,0.8,0.8,"0.2*0.2*0.8*0.8 =",2.5600000000000008E-2,null,null,null,{"$f":"SUM(P15:P19)","v":1.0000000000000002}]
[7,"S","NS","NS","S",2,{"$f":"IF(B21:E21=$C$6,$B$1,$B$2)","v":0.2},0.8,0.8,0.2,"0.2*0.8*0.8*0.2 =",2.5600000000000008E-2]
[8,"NS","NS","S","S",2,{"$f":"IF(B22:E22=$C$6,$B$1,$B$2)","v":0.8},0.8,0.2,0.2,"0.8*0.8*0.2*0.2 =",2.5600000000000008E-2,null,null,"E(x)",{"$f":"SUMPRODUCT(N15:N19,P15:P19)","v":0.80000000000000016},{"$f":"B3*B1","v":0.8}]
[9,"S","NS","S","NS",2,{"$f":"IF(B23:E23=$C$6,$B$1,$B$2)","v":0.2},0.8,0.2,0.8,"0.2*0.8*0.2*0.8 =",2.5600000000000008E-2,null,null,"SD",{"$f":"SQRT(SUMPRODUCT((N15:N19-P22)^2,P15:P19))","v":0.8},{"$f":"SQRT(Q22*(1-B1))","v":0.8}]
[10,"NS","S","NS","S",2,{"$f":"IF(B24:E24=$C$6,$B$1,$B$2)","v":0.8},0.2,0.8,0.2,"0.8*0.2*0.8*0.2 =",2.5600000000000008E-2]
[11,"NS","S","S","NS",2,{"$f":"IF(B25:E25=$C$6,$B$1,$B$2)","v":0.8},0.2,0.2,0.8,"0.8*0.2*0.2*0.8 =",2.5600000000000008E-2]
[12,"S","NS","NS","NS",1,{"$f":"IF(B26:E26=$C$6,$B$1,$B$2)","v":0.2},0.8,0.8,0.8,"0.2*0.8*0.8*0.8 =",0.10240000000000003]
[13,"NS","S","NS","NS",1,{"$f":"IF(B27:E27=$C$6,$B$1,$B$2)","v":0.8},0.2,0.8,0.8,"0.8*0.2*0.8*0.8 =",0.10240000000000003]
[14,"NS","NS","S","NS",1,{"$f":"IF(B28:E28=$C$6,$B$1,$B$2)","v":0.8},0.8,0.2,0.8,"0.8*0.8*0.2*0.8 =",0.10240000000000003]
[15,"NS","NS","NS","S",1,{"$f":"IF(B29:E29=$C$6,$B$1,$B$2)","v":0.8},0.8,0.8,0.2,"0.8*0.8*0.8*0.2 =",0.10240000000000003]
[16,"NS","NS","NS","NS",0,{"$f":"IF(B30:E30=$C$6,$B$1,$B$2)","v":0.8},0.8,0.8,0.8,"0.8*0.8*0.8*0.8 =",0.40960000000000013]

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[]
[null,"n = # of Fixed Trials = Appointments",null,null,null,4]
[null,"p = Prob of Success =",null,null,null,0.2]
[null,{"$f":"\"Random Discrete Variable = x = # Sales in \"&F2&\" Tries\"","v":"Random Discrete Variable = x = # Sales in 4 Tries"},null,null,null,3]
[]
[null,"Success is?","Sale","S"]
[null,"Not?","Not Sale","NS"]
[]
[null,"Sample Points for 3 sales in 4 tries:",null,null,null,null,null,null,null,null,null,null,"Chapter 4 Methods with AND and OR:"]
[]
[null,"Sample Point","1st","2nd","3rd","4th","X","1st","2nd","3rd","4th","AND Logical Test","Multiplication Rule"]
[null,"SP1",{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$7","v":"NS"},{"$f":"COUNTIF(C12:F12,$D$6)","v":3},{"$f":"IF(C12:F12=$D$6,$F$3,1-$F$3)","v":0.2},0.2,0.2,0.8,{"$f":"\"P(\"&C12:C15&\" AND \"&D12:D15&\" AND \"&E12:E15&\" AND \"&F12:F15&\")\"","v":"P(S AND S AND S AND NS)"},{"$f":"H12:H15&\"*\"&I12:I15&\"*\"&J12:J15&\"*\"&K12:K15&\" =\"","v":"0.2*0.2*0.2*0.8 ="},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(N12),COLUMN(N12),4)&\": \"&_xlfn.FORMULATEXT(N12),\"\")","v":""}]
[null,"SP2",{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$7","v":"NS"},{"$f":"$D$6","v":"S"},{"$f":"COUNTIF(C13:F13,$D$6)","v":3},{"$f":"IF(C13:F13=$D$6,$F$3,1-$F$3)","v":0.2},0.2,0.8,0.2,"P(S AND S AND NS AND S)","0.2*0.2*0.8*0.2 ="]
[null,"SP3",{"$f":"$D$6","v":"S"},{"$f":"$D$7","v":"NS"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"COUNTIF(C14:F14,$D$6)","v":3},{"$f":"IF(C14:F14=$D$6,$F$3,1-$F$3)","v":0.2},0.8,0.2,0.2,"P(S AND NS AND S AND S)","0.2*0.8*0.2*0.2 ="]
[null,"SP4",{"$f":"$D$7","v":"NS"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"COUNTIF(C15:F15,$D$6)","v":3},{"$f":"IF(C15:F15=$D$6,$F$3,1-$F$3)","v":0.8},0.2,0.2,0.2,"P(NS AND S AND S AND S)","0.8*0.2*0.2*0.2 ="]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(\"&_xlfn.TEXTJOIN(\" OR \",,B12:B15)&\")\"","v":"P(SP1 OR SP2 OR SP3 OR SP4)"},{"$f":"\"P(x = \"&$F$4&\")\"","v":"P(x = 3)"},null,"< = OR Logical Test = Addition Rule"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Binomial Probability Math Formula:"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"P(X)","P(X)"]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(x = \"&$F$4&\")\"","v":"P(x = 3)"},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(N21),COLUMN(N21),4)&\": \"&_xlfn.FORMULATEXT(N21),\"\")","v":""}]
[]
[]
[null,null,null,null,null," ",null,null,null,null,null,null,"Excel Built-in Function: BINOM.DIST.RANGE"]
[]
[null,"Variable",null,null,null,null,null,null,"Function argument",null,null,null,"P(X)","P(X)"]
[null,"n = # of Fixed Trials =",null,null,null,null,null,null,"trials",null,null,null,{"$f":"\"P(x = \"&$F$4&\")\"","v":"P(x = 3)"},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(N27),COLUMN(N27),4)&\": \"&_xlfn.FORMULATEXT(N27),\"\")","v":""}]
[null,"p = Prob of Success =",null,null,null,null,null,null,"probability_s"]
[null,"Random Discrete Variable that counts successes = x. If you use only this argument, it calculates the probability of exactly x.",null,null,null,null,null,null,"number_s"]
[null,"This is second x value. If you use this argument with the first x value in number_s argument, the function will calculate the probability between the two x values, inclusive.",null,null,null,null,null,null,"[number_s2]"]

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[]
[null,"n = # of Fixed Trials = Appointments",null,null,null,4]
[null,"p = Prob of Success =",null,null,null,0.2]
[null,{"$f":"\"Random Discrete Variable = x = # Sales in \"&F2&\" Tries\"","v":"Random Discrete Variable = x = # Sales in 4 Tries"},null,null,null,3]
[]
[null,"Success is?","Sale","S"]
[null,"Not?","Not Sale","NS"]
[]
[null,"Sample Points for 3 sales in 4 tries:",null,null,null,null,null,null,null,null,null,null,"Chapter 4 Methods with AND and OR:"]
[]
[null,"Sample Point","1st","2nd","3rd","4th","X","1st","2nd","3rd","4th","AND Logical Test","Multiplication Rule"]
[null,"SP1",{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$7","v":"NS"},{"$f":"COUNTIF(C12:F12,$D$6)","v":3},{"$f":"IF(C12:F12=$D$6,$F$3,1-$F$3)","v":0.2},0.2,0.2,0.8,{"$f":"\"P(\"&C12:C15&\" AND \"&D12:D15&\" AND \"&E12:E15&\" AND \"&F12:F15&\")\"","v":"P(S AND S AND S AND NS)"},{"$f":"H12:H15&\"*\"&I12:I15&\"*\"&J12:J15&\"*\"&K12:K15&\" =\"","v":"0.2*0.2*0.2*0.8 ="},{"$f":"PRODUCT(_xlfn.ANCHORARRAY(H12))","v":6.400000000000002E-3},{"$f":"_xlfn.IFNA(ADDRESS(ROW(N12),COLUMN(N12),4)&\": \"&_xlfn.FORMULATEXT(N12),\"\")","v":"N12: =PRODUCT(H12#)"}]
[null,"SP2",{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$7","v":"NS"},{"$f":"$D$6","v":"S"},{"$f":"COUNTIF(C13:F13,$D$6)","v":3},{"$f":"IF(C13:F13=$D$6,$F$3,1-$F$3)","v":0.2},0.2,0.8,0.2,"P(S AND S AND NS AND S)","0.2*0.2*0.8*0.2 =",{"$f":"PRODUCT(_xlfn.ANCHORARRAY(H13))","v":6.400000000000002E-3}]
[null,"SP3",{"$f":"$D$6","v":"S"},{"$f":"$D$7","v":"NS"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"COUNTIF(C14:F14,$D$6)","v":3},{"$f":"IF(C14:F14=$D$6,$F$3,1-$F$3)","v":0.2},0.8,0.2,0.2,"P(S AND NS AND S AND S)","0.2*0.8*0.2*0.2 =",6.400000000000002E-3]
[null,"SP4",{"$f":"$D$7","v":"NS"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"$D$6","v":"S"},{"$f":"COUNTIF(C15:F15,$D$6)","v":3},{"$f":"IF(C15:F15=$D$6,$F$3,1-$F$3)","v":0.8},0.2,0.2,0.2,"P(NS AND S AND S AND S)","0.8*0.2*0.2*0.2 =",6.400000000000002E-3]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(\"&_xlfn.TEXTJOIN(\" OR \",,B12:B15)&\")\"","v":"P(SP1 OR SP2 OR SP3 OR SP4)"},{"$f":"\"P(x = \"&$F$4&\")\"","v":"P(x = 3)"},{"$f":"SUM(N12:N15)","v":2.5600000000000008E-2},"< = OR Logical Test = Addition Rule"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Binomial Probability Math Formula:"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"P(X)","P(X)"]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"P(x = \"&$F$4&\")\"","v":"P(x = 3)"},{"$f":"COMBIN(F2,F4)*F3^F4*(1-F3)^(F2-F4)","v":2.5600000000000008E-2},{"$f":"_xlfn.IFNA(ADDRESS(ROW(N21),COLUMN(N21),4)&\": \"&_xlfn.FORMULATEXT(N21),\"\")","v":"N21: =COMBIN(F2,F4)*F3^F4*(1-F3)^(F2-F4)"}]
[]
[]
[null,null,null,null,null," ",null,null,null,null,null,null,"Excel Built-in Function: BINOM.DIST.RANGE"]
[]
[null,"Variable",null,null,null,null,null,null,"Function argument",null,null,null,"P(X)","P(X)"]
[null,"n = # of Fixed Trials =",null,null,null,null,null,null,"trials",null,null,null,{"$f":"\"P(x = \"&$F$4&\")\"","v":"P(x = 3)"},{"$f":"_xlfn.BINOM.DIST.RANGE(F2,F3,F4)","v":2.5600000000000005E-2},{"$f":"_xlfn.IFNA(ADDRESS(ROW(N27),COLUMN(N27),4)&\": \"&_xlfn.FORMULATEXT(N27),\"\")","v":"N27: =BINOM.DIST.RANGE(F2,F3,F4)"}]
[null,"p = Prob of Success =",null,null,null,null,null,null,"probability_s"]
[null,"Random Discrete Variable that counts successes = x. If you use only this argument, it calculates the probability of exactly x.",null,null,null,null,null,null,"number_s"]
[null,"This is second x value. If you use this argument with the first x value in number_s argument, the function will calculate the probability between the two x values, inclusive.",null,null,null,null,null,null,"[number_s2]"]

{"sheet":"B(2)","index":27,"n_rows":47,"n_cols":22,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["An insurance agent has appointments with 4 clients tomorrow."]
["From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 4, p = 0.2"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = Appointments",null,null,null,4]
["p = Prob of Success =",null,null,null,0.2]
[{"$f":"\"Random Discrete Variable = x = # Sales in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = # Sales in 4 Tries"},null,null,null,3]
["Mean = µ = E(x) = Expected Value ="]
["Mean = µ = E(x) = Expected Value ="]
["Standard Deviation = s ="]
["Standard Deviation = s ="]
[]
["X","P(x) = f(x)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(x) = f(x)","P(x) = f(x)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"FACT(E9)/(FACT(A18:A22)*FACT(E9-A18:A22))*E10^A18:A22*(1-E10)^(E9-A18:A22)","v":0.40960000000000019},{"$f":"COMBIN(E9,A18:A22)*E10^A18:A22*(1-E10)^(E9-A18:A22)","v":0.40960000000000019},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(S18),COLUMN(S18),4)&\": \"&_xlfn.FORMULATEXT(S18),\"\")","v":"S18: =FACT(E9)/(FACT(A18:A22)*FACT(E9-A18:A22))*E10^A18:A22*(1-E10)^(E9-A18:A22)"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.40960000000000019,0.40960000000000019,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(T18),COLUMN(T18),4)&\": \"&_xlfn.FORMULATEXT(T18),\"\")","v":"T18: =COMBIN(E9,A18:A22)*E10^A18:A22*(1-E10)^(E9-A18:A22)"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.40960000000000019,0.40960000000000019]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.40960000000000019,0.40960000000000019]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.40960000000000019,0.40960000000000019]
["Total",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Total",{"$f":"SUM(S18:S22)","v":2.0480000000000009},{"$f":"SUM(T18:T22)","v":2.0480000000000009}]
[]
["P(x) = f(x)","P(x) = f(x)","SUM",null,"Lower X","Upper X"]
[{"$f":"\"P(x = \"&E26&\")\"","v":"P(x = 2)"},null,null,null,2,2,{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E26:E30,F26:F30)","v":0.15359999999999996}]
[{"$f":"\"P(x > \"&E27-1&\")\"","v":"P(x > 1)"},null,null,null,2,4,0.18080000000000007]
[{"$f":"\"P(x >= \"&E28&\")\"","v":"P(x >= 3)"},null,null,null,3,4,2.7200000000000016E-2]
[{"$f":"\"P(x < \"&F29+1&\")\"","v":"P(x < 3)"},null,null,null,0,2,0.9728]
[{"$f":"\"P(x <= \"&F30&\")\"","v":"P(x <= 3)"},null,null,null,0,3,0.99839999999999995]
[{"$f":"\"P(x <= \"&E31&\")\"","v":"P(x <= 3)"},null,null,null,3]
[]
[]
[]
[]
[]
[]
[]
[null,"If we had all the data:"]
[]
[null,"Average Policies Sold in 4 Tries:",null,null,{"$f":"AVERAGE(C46:G4142)","v":{"$error":"#REF!"}}]
[null,"Standard Deviation Pop:",null,null,{"$f":"_xlfn.STDEV.P(C46:G4142)","v":{"$error":"#REF!"}}]
[null,"Count:",null,null,{"$f":"COUNT(C47:G4142)","v":0},{"$f":"SUM(_xlfn.ANCHORARRAY(C45))","v":{"$error":"#REF!"}}]
[]
[null,"# Times:",{"$f":"TRANSPOSE(_xlfn.ANCHORARRAY(B18))*10000","v":{"$error":"#REF!"}}]
[null,"X:",{"$f":"_xlfn.SEQUENCE(,E9+1,0)","v":0},1,2,3,4]
[null,"Data:",{"$f":"_xlfn.SEQUENCE(C45,,C46,0)","v":{"$error":"#REF!"}},{"$f":"_xlfn.SEQUENCE(D45,,D46,0)","v":{"$error":"#VALUE!"}},{"$f":"_xlfn.SEQUENCE(E45,,E46,0)","v":{"$error":"#VALUE!"}},{"$f":"_xlfn.SEQUENCE(F45,,F46,0)","v":{"$error":"#VALUE!"}},{"$f":"_xlfn.SEQUENCE(G45,,G46,0)","v":{"$error":"#VALUE!"}}]

{"sheet":"B(2an)","index":28,"n_rows":4142,"n_cols":22,"rows_kept":4142,"cut":false,"hidden":false,"merged":[]}
["An insurance agent has appointments with 4 clients tomorrow."]
["From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 4, p = 0.2"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = Appointments",null,null,null,4]
["p = Prob of Success =",null,null,null,0.2]
[{"$f":"\"Random Discrete Variable = x = # Sales in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = # Sales in 4 Tries"},null,null,null,3]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"SUMPRODUCT(_xlfn.ANCHORARRAY(A18),_xlfn.ANCHORARRAY(B18))","v":0.79999999999999982},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E12),COLUMN(E12),4)&\": \"&_xlfn.FORMULATEXT(E12),\"\")","v":"E12: =SUMPRODUCT(A18#,B18#)"}]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"E9*E10","v":0.8},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E13),COLUMN(E13),4)&\": \"&_xlfn.FORMULATEXT(E13),\"\")","v":"E13: =E9*E10"}]
["Standard Deviation = s =",null,null,null,{"$f":"SQRT(SUMPRODUCT((_xlfn.ANCHORARRAY(A18)-E12)^2,_xlfn.ANCHORARRAY(B18)))","v":0.79999999999999993},null,"E14: =SQRT(SUMPRODUCT((A18#-E12)^2,B18#))"]
["Standard Deviation = s =",null,null,null,{"$f":"SQRT(E9*E10*(1-E10))","v":0.8},null,"E15: =SQRT(E9*E10*(1-E10))"]
[]
["X","P(x) = f(x)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(x) = f(x)","P(x) = f(x)"]
[{"$f":"_xlfn.SEQUENCE(E9+1,,0)","v":0},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,_xlfn.ANCHORARRAY(A18))","v":0.40959999999999996},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(A18),COLUMN(A18),4)&\": \"&_xlfn.FORMULATEXT(A18),\"\")","v":"A18: =SEQUENCE(E9+1,,0)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"FACT(E9)/(FACT(A18:A22)*FACT(E9-A18:A22))*E10^A18:A22*(1-E10)^(E9-A18:A22)","v":0.40960000000000019},{"$f":"COMBIN(E9,A18:A22)*E10^A18:A22*(1-E10)^(E9-A18:A22)","v":0.40960000000000019},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(S18),COLUMN(S18),4)&\": \"&_xlfn.FORMULATEXT(S18),\"\")","v":"S18: =FACT(E9)/(FACT(A18:A22)*FACT(E9-A18:A22))*E10^A18:A22*(1-E10)^(E9-A18:A22)"}]
[1,0.40959999999999996,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B18),COLUMN(B18),4)&\": \"&_xlfn.FORMULATEXT(B18),\"\")","v":"B18: =BINOM.DIST.RANGE(E9,E10,A18#)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.40960000000000013,0.40960000000000013,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(T18),COLUMN(T18),4)&\": \"&_xlfn.FORMULATEXT(T18),\"\")","v":"T18: =COMBIN(E9,A18:A22)*E10^A18:A22*(1-E10)^(E9-A18:A22)"}]
[2,0.15359999999999996,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.15360000000000007,0.15360000000000007]
[3,2.5600000000000005E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.5600000000000008E-2,2.5600000000000008E-2]
[4,1.6000000000000005E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6000000000000007E-3,1.6000000000000007E-3]
["Total",{"$f":"SUM(_xlfn.ANCHORARRAY(B18))","v":0.99999999999999989},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Total",{"$f":"SUM(S18:S22)","v":1.0000000000000004},{"$f":"SUM(T18:T22)","v":1.0000000000000004}]
[]
["P(x) = f(x)","P(x) = f(x)","SUM",null,"Lower X","Upper X","P(x) = f(x) Spilled"]
[{"$f":"\"P(x = \"&E26&\")\"","v":"P(x = 2)"},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E26)","v":0.15359999999999996},{"$f":"B20","v":0.15359999999999996},null,2,2,{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E26:E30,F26:F30)","v":0.15359999999999996},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(G26),COLUMN(G26),4)&\": \"&_xlfn.FORMULATEXT(G26),\"\")","v":"G26: =BINOM.DIST.RANGE(E9,E10,E26:E30,F26:F30)"}]
[{"$f":"\"P(x > \"&E27-1&\")\"","v":"P(x > 1)"},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E27,F27)","v":0.18080000000000007},{"$f":"SUM(B20:B22)","v":0.18079999999999996},null,2,4,0.18080000000000007]
[{"$f":"\"P(x >= \"&E28&\")\"","v":"P(x >= 3)"},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E28,F28)","v":2.7200000000000016E-2},{"$f":"SUM(B21:B22)","v":2.7200000000000005E-2},null,3,4,2.7200000000000016E-2]
[{"$f":"\"P(x < \"&F29+1&\")\"","v":"P(x < 3)"},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E29,F29)","v":0.9728},{"$f":"SUM(B18:B20)","v":0.97279999999999989},null,0,2,0.9728]
[{"$f":"\"P(x <= \"&F30&\")\"","v":"P(x <= 3)"},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,E30,F30)","v":0.99839999999999995},{"$f":"SUM(B18:B21)","v":0.99839999999999984},null,0,3,0.99839999999999995]
[{"$f":"\"P(x <= \"&E31&\")\"","v":"P(x <= 3)"},{"$f":"_xlfn.BINOM.DIST(E31,E9,E10,TRUE)","v":0.99839999999999995},null,null,3]
[]
[{"$f":"_xlfn.IFNA(ADDRESS(ROW(B26),COLUMN(B26),4)&\": \"&_xlfn.FORMULATEXT(B26),\"\")","v":"B26: =BINOM.DIST.RANGE(E9,E10,E26)"},null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C26),COLUMN(C26),4)&\": \"&_xlfn.FORMULATEXT(C26),\"\")","v":"C26: =B20"}]
[null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C27),COLUMN(C27),4)&\": \"&_xlfn.FORMULATEXT(C27),\"\")","v":"C27: =SUM(B20:B22)"}]
[null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C28),COLUMN(C28),4)&\": \"&_xlfn.FORMULATEXT(C28),\"\")","v":"C28: =SUM(B21:B22)"}]
[null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C29),COLUMN(C29),4)&\": \"&_xlfn.FORMULATEXT(C29),\"\")","v":"C29: =SUM(B18:B20)"}]
[null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(C30),COLUMN(C30),4)&\": \"&_xlfn.FORMULATEXT(C30),\"\")","v":"C30: =SUM(B18:B21)"}]
[]
[null,"If we had all the data:"]
[]
[null,"Average Policies Sold in 4 Tries:",null,null,{"$f":"AVERAGE(C46:G4142)","v":0.80059970014992499}]
[null,"Standard Deviation Pop:",null,null,{"$f":"_xlfn.STDEV.P(C46:G4142)","v":0.80087386067317445}]
[null,"Count:",null,null,{"$f":"COUNT(C47:G4142)","v":10000},{"$f":"SUM(_xlfn.ANCHORARRAY(C45))","v":9999.9999999999982}]
[]
[null,"# Times:",{"$f":"TRANSPOSE(_xlfn.ANCHORARRAY(B18))*10000","v":4095.9999999999995},4095.9999999999995,1535.9999999999995,256.00000000000006,16.000000000000004]
[null,"X:",{"$f":"_xlfn.SEQUENCE(,E9+1,0)","v":0},1,2,3,4]
[null,"Data:",{"$f":"_xlfn.SEQUENCE(C45,,C46,0)","v":0},{"$f":"_xlfn.SEQUENCE(D45,,D46,0)","v":1},{"$f":"_xlfn.SEQUENCE(E45,,E46,0)","v":2},{"$f":"_xlfn.SEQUENCE(F45,,F46,0)","v":3},{"$f":"_xlfn.SEQUENCE(G45,,G46,0)","v":4}]
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{"sheet":"B(3)","index":29,"n_rows":23,"n_cols":8,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["A flight from Oakland to Seattle occurs 6 times per day. The probability that any 1 flight is late is 10%. "]
["What is the probability that exactly 2 planes are late? Less than 2 are late? What is the mean and standard deviation?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 6, p = 0.1"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials =# flights",null,null,null,6]
["p = Prob of Success =",null,null,null,0.1]
[{"$f":"\"Random Discrete Variable = x = Planes Late in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Planes Late in 6 Tries"},null,null,null,2]
["Mean = µ = E(x) = Expected Value ="]
["Standard Deviation = s ="]
[]
["X","P(x) = f(x)",null,"P(x) = f(x)","P(x) = f(x)","SUM","Lower X","Upper X"]
[null,null,null,{"$f":"\"P(x = \"&E11&\")\"","v":"P(x = 2)"},null,null,2,2]
[null,null,null,{"$f":"\"P(x <= \"&E11&\")\"","v":"P(x <= 2)"},null,null,0,2]
[null,null,null,{"$f":"\"P(x < \"&E11&\")\"","v":"P(x < 2)"},null,null,0,1]
[null,null,null,{"$f":"\"P(x >= \"&E11&\")\"","v":"P(x >= 2)"},null,null,2,6]
[null,null,null,{"$f":"\"P(x > \"&E11&\")\"","v":"P(x > 2)"},null,null,3,6]
[]
[null,null,null,"X =",2]
["Total"]

{"sheet":"B(3an)","index":30,"n_rows":23,"n_cols":18,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["A flight from Oakland to Seattle occurs 6 times per day. The probability that any 1 flight is late is 10%. "]
["What is the probability that exactly 2 planes are late? Less than 2 are late? What is the mean and standard deviation?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 6, p = 0.1"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials =# flights",null,null,null,6]
["p = Prob of Success =",null,null,null,0.1]
[{"$f":"\"Random Discrete Variable = x = Planes Late in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Planes Late in 6 Tries"},null,null,null,2,null,null,null,null,null,null,"Formulas Used:"]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"E9*E10","v":0.60000000000000009},null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E12),COLUMN(E12),4)&\": \"&_xlfn.FORMULATEXT(E12),\"\")","v":"E12: =E9*E10"}]
["Standard Deviation = s =",null,null,null,{"$f":"SQRT(E12*(1-E10))","v":0.73484692283495356},null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E13),COLUMN(E13),4)&\": \"&_xlfn.FORMULATEXT(E13),\"\")","v":"E13: =SQRT(E12*(1-E10))"}]
[]
["X","P(x) = f(x)",null,"P(x) = f(x)","P(x) = f(x)","SUM","Lower X","Upper X"]
[{"$f":"_xlfn.SEQUENCE(E9+1,,0)","v":0},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,A16:A22)","v":0.53144100000000005},null,{"$f":"\"P(x = \"&E11&\")\"","v":"P(x = 2)"},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,G16:G20,H16:H20)","v":9.8415000000000002E-2},{"$f":"SUM(B18)","v":9.8415000000000002E-2},2,2,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(A16),COLUMN(A16),4)&\": \"&_xlfn.FORMULATEXT(A16),\"\")","v":"A16: =SEQUENCE(E9+1,,0)"},null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F16),COLUMN(F16),4)&\": \"&_xlfn.FORMULATEXT(F16),\"\")","v":"F16: =SUM(B18)"}]
[1,0.354294,null,{"$f":"\"P(x <= \"&E11&\")\"","v":"P(x <= 2)"},0.98414999999999997,{"$f":"SUM(B16:B18)","v":0.98415000000000008},0,2,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B16),COLUMN(B16),4)&\": \"&_xlfn.FORMULATEXT(B16),\"\")","v":"B16: =BINOM.DIST.RANGE(E9,E10,A16:A22)"},null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F17),COLUMN(F17),4)&\": \"&_xlfn.FORMULATEXT(F17),\"\")","v":"F17: =SUM(B16:B18)"}]
[2,9.8415000000000002E-2,null,{"$f":"\"P(x < \"&E11&\")\"","v":"P(x < 2)"},0.88573499999999994,{"$f":"SUM(B16:B17)","v":0.88573500000000005},0,1,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E16),COLUMN(E16),4)&\": \"&_xlfn.FORMULATEXT(E16),\"\")","v":"E16: =BINOM.DIST.RANGE(E9,E10,G16:G20,H16:H20)"},null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F18),COLUMN(F18),4)&\": \"&_xlfn.FORMULATEXT(F18),\"\")","v":"F18: =SUM(B16:B17)"}]
[3,1.4580000000000011E-2,null,{"$f":"\"P(x >= \"&E11&\")\"","v":"P(x >= 2)"},0.11426500000000006,{"$f":"SUM(B18:B22)","v":0.11426500000000002},2,6,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F19),COLUMN(F19),4)&\": \"&_xlfn.FORMULATEXT(F19),\"\")","v":"F19: =SUM(B18:B22)"}]
[4,1.2150000000000012E-3,null,{"$f":"\"P(x > \"&E11&\")\"","v":"P(x > 2)"},1.5850000000000013E-2,{"$f":"SUM(B19:B22)","v":1.5850000000000013E-2},3,6,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(F20),COLUMN(F20),4)&\": \"&_xlfn.FORMULATEXT(F20),\"\")","v":"F20: =SUM(B19:B22)"}]
[5,5.3999999999999998E-5]
[6,1.0000000000000004E-6,null,"X =",2]
["Total"]

{"sheet":"B(4)","index":31,"n_rows":26,"n_cols":7,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
["The probability of getting stuck in traffic on the West Seattle Bridge in the morning is 0.15."]
["Over the next two weeks (10 workdays), what is probability that you will get stuck in traffic 0 times? 1 Time?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 10, p = 0.15"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # drive on bridge",null,null,null,10]
["p = Prob of Success =",null,null,null,0.15]
[{"$f":"\"Random Discrete Variable = x = Stuck In Traffic in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Stuck In Traffic in 10 Tries"}]
["Mean = µ = E(x) = Expected Value ="]
[]
["X","P(x) = f(x)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Total"]

{"sheet":"B(4an)","index":32,"n_rows":26,"n_cols":7,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
["The probability of getting stuck in traffic on the West Seattle Bridge in the morning is 0.15."]
["Over the next two weeks (10 workdays), what is probability that you will get stuck in traffic 0 times? 1 Time?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 10, p = 0.15"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # drive on bridge",null,null,null,10]
["p = Prob of Success =",null,null,null,0.15]
[{"$f":"\"Random Discrete Variable = x = Stuck In Traffic in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Stuck In Traffic in 10 Tries"},null,null,null,null,null,"Formulas:"]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"E9*E10","v":1.5},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E12),COLUMN(E12),4)&\": \"&_xlfn.FORMULATEXT(E12),\"\")","v":"E12: =E9*E10"}]
[]
["X","P(x) = f(x)"]
[{"$f":"_xlfn.SEQUENCE(E9+1,,0)","v":0},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,A15:A25)","v":0.1968744043407227},null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(A15),COLUMN(A15),4)&\": \"&_xlfn.FORMULATEXT(A15),\"\")","v":"A15: =SEQUENCE(E9+1,,0)"}]
[1,0.3474254194248047,null,null,null,null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(B15),COLUMN(B15),4)&\": \"&_xlfn.FORMULATEXT(B15),\"\")","v":"B15: =BINOM.DIST.RANGE(E9,E10,A15:A25)"}]
[2,0.27589665660205087]
[3,0.12983372075390626]
[4,4.0095707879882835E-2]
[5,8.4908557863281192E-3]
[6,1.2486552626953143E-3]
[7,1.2591481640624995E-4]
[8,8.3325981445312545E-6]
[9,3.267685546874998E-7]
[10,5.7665039062500008E-9]
["Total"]

{"sheet":"B(5)","index":33,"n_rows":15,"n_cols":5,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Highline found that 16.00% of its students withdraw from Accounting 202."]
["In the current class that has 35 students enrolled, what is the probability that between 3 and 7 students withdraw? What is the mean?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes"]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # Students",null,null,null,35]
["p = Prob of Success = Withdraw",null,null,null,0.16]
[{"$f":"\"Random Discrete Variable = x = withdraw from class in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = withdraw from class in 35 Tries"}]
["Mean = µ = E(x) = Expected Value ="]
[]
[null,"X1","X2","P(Event)","P(Event)"]
[null,3,7,"P(3 <= X <= 7)"]

{"sheet":"B(5an)","index":34,"n_rows":15,"n_cols":7,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
["Highline found that 16.00% of its students withdraw from Accounting 202."]
["In the current class that has 35 students enrolled, what is the probability that between 3 and 7 students withdraw? What is the mean?"]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes"]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # Students",null,null,null,35]
["p = Prob of Success = Withdraw",null,null,null,0.16]
[{"$f":"\"Random Discrete Variable = x = withdraw from class in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = withdraw from class in 35 Tries"}]
["Mean = µ = E(x) = Expected Value =",null,null,null,{"$f":"E10*E9","v":5.6000000000000005},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E12),COLUMN(E12),4)&\": \"&_xlfn.FORMULATEXT(E12),\"\")","v":"E12: =E10*E9"}]
[]
[null,"X1","X2","P(Event)","P(Event)"]
[null,3,7,"P(3 <= X <= 7)",{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,B15,C15)","v":0.74787661716250275},null,{"$f":"_xlfn.IFNA(ADDRESS(ROW(E15),COLUMN(E15),4)&\": \"&_xlfn.FORMULATEXT(E15),\"\")","v":"E15: =BINOM.DIST.RANGE(E9,E10,B15,C15)"}]

{"sheet":"B(6)","index":35,"n_rows":16,"n_cols":5,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["n",5,null,null,{"$f":"\"Binomial Distribution, n = \"&B1&\" p = \"&B2","v":"Binomial Distribution, n = 5 p = 0.5"}]
["p",0.5]
[]
[]
["X","P(x)"]
[{"$f":"_xlfn.SEQUENCE(B1+1,,0)","v":0},{"$f":"_xlfn.BINOM.DIST.RANGE(B1,B2,_xlfn.ANCHORARRAY(A6))","v":3.125E-2}]
[1,0.15624999999999992]
[2,0.3125]
[3,0.3125]
[4,0.15624999999999992]
[5,3.125E-2]
[]
[]
[null,null,null,null,"As n increases, distributions approached Bell Shape"]
[null,null,null,null,"As p approaches 0.5, distributions approached Bell Shape"]
[null,null,null,null,"At p = .5, distribution is Bell"]

{"sheet":"<=","index":36,"n_rows":31,"n_cols":7,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
[{"$f":"\"The probability of getting stuck in traffic on Hwy 99 in the morning is \"&E10&\".\"","v":"The probability of getting stuck in traffic on Hwy 99 in the morning is 0.25."}]
[{"$f":"\"Over the next three weeks (\"&E9&\" workdays), what is probability that you will get stuck in traffic for various x values\"","v":"Over the next three weeks (15 workdays), what is probability that you will get stuck in traffic for various x values"}]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 15, p = 0.25"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # drive on bridge",null,null,null,15]
["p = Prob of Success =",null,null,null,0.25]
[{"$f":"\"Random Discrete Variable = x = Stuck In Traffic in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Stuck In Traffic in 15 Tries"},null,null,null,4]
[{"$f":"\"P(x<=\"&$E$11&\")\"","v":"P(x<=4)"},null,null,null,{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,0,E11)","v":0.68648594152182341}]
[]
["X","P(x) = f(x)",{"$f":"\"P(x<=\"&$E$11&\") = \"&ROUND(E12,4)","v":"P(x<=4) = 0.6865"}]
[{"$f":"_xlfn.SEQUENCE(E9+1,,0)","v":0},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,_xlfn.ANCHORARRAY(A15))","v":1.3363461010158065E-2},{"$f":"IF(_xlfn.ANCHORARRAY(A15)<=E11,_xlfn.ANCHORARRAY(B15),\"\")","v":1.3363461010158065E-2}]
[1,6.6817305050790338E-2,6.6817305050790338E-2]
[2,0.15590704511851075,0.15590704511851075]
[3,0.22519906517118218,0.22519906517118218]
[4,0.22519906517118218,0.22519906517118218]
[5,0.16514598112553358,""]
[6,9.1747767291963059E-2,""]
[7,3.9320471696555608E-2,""]
[8,1.3106823898851871E-2,""]
[9,3.398065455257893E-3,""]
[10,6.7961309105157863E-4,""]
[11,1.0297168046236046E-4,""]
[12,1.1441297829151157E-5,""]
[13,8.8009983301163059E-7,""]
[14,4.1909515857696467E-8,""]
[15,9.3132257461547934E-10,""]
["Total",{"$f":"SUM(B15:B30)","v":1}]

{"sheet":">","index":37,"n_rows":31,"n_cols":7,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
[{"$f":"\"The probability of getting stuck in traffic on Hwy 99 in the morning is \"&E10&\".\"","v":"The probability of getting stuck in traffic on Hwy 99 in the morning is 0.25."}]
[{"$f":"\"Over the next three weeks (\"&E9&\" workdays), what is probability that you will get stuck in traffic for various x values\"","v":"Over the next three weeks (15 workdays), what is probability that you will get stuck in traffic for various x values"}]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 15, p = 0.25"}]
[2,"Each trial only results in S or F",null,null,"Yes"]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # drive on bridge",null,null,null,15]
["p = Prob of Success =",null,null,null,0.25]
[{"$f":"\"Random Discrete Variable = x = Stuck In Traffic in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Stuck In Traffic in 15 Tries"},null,null,null,3]
[{"$f":"C14","v":"P(x>3) = 0.5387"},null,null,null,{"$f":"1-_xlfn.BINOM.DIST(E11,E9,E10,1)","v":0.53871312364935886}]
[]
["X","P(x) = f(x)",{"$f":"\"P(x>\"&E11&\") = \"&ROUND(E12,4)","v":"P(x>3) = 0.5387"}]
[{"$f":"_xlfn.SEQUENCE(E9+1,,0)","v":0},{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,_xlfn.ANCHORARRAY(A15))","v":1.3363461010158065E-2},{"$f":"IF(_xlfn.ANCHORARRAY(A15)>E11,_xlfn.ANCHORARRAY(B15),\"\")","v":""}]
[1,6.6817305050790338E-2,""]
[2,0.15590704511851075,""]
[3,0.22519906517118218,""]
[4,0.22519906517118218,0.22519906517118218]
[5,0.16514598112553358,0.16514598112553358]
[6,9.1747767291963059E-2,9.1747767291963059E-2]
[7,3.9320471696555608E-2,3.9320471696555608E-2]
[8,1.3106823898851871E-2,1.3106823898851871E-2]
[9,3.398065455257893E-3,3.398065455257893E-3]
[10,6.7961309105157863E-4,6.7961309105157863E-4]
[11,1.0297168046236046E-4,1.0297168046236046E-4]
[12,1.1441297829151157E-5,1.1441297829151157E-5]
[13,8.8009983301163059E-7,8.8009983301163059E-7]
[14,4.1909515857696467E-8,4.1909515857696467E-8]
[15,9.3132257461547934E-10,9.3132257461547934E-10]
["Total",{"$f":"SUM(B15:B30)","v":1}]

{"sheet":"Between","index":38,"n_rows":32,"n_cols":7,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
[{"$f":"\"The probability of getting stuck in traffic on Hwy 99 in the morning is \"&E10&\".\"","v":"The probability of getting stuck in traffic on Hwy 99 in the morning is 0.25."}]
[{"$f":"\"Over the next three weeks (\"&E9&\" workdays), what is probability that you will get stuck in traffic for various x values/\"","v":"Over the next three weeks (15 workdays), what is probability that you will get stuck in traffic for various x values/"}]
["Binomial Experiment?"]
[1,"Fixed # of Identical Trials = n",null,null,"Yes",null,{"$f":"\"Binomial Distribution, n = \"&E9&\", p = \"&E10","v":"Binomial Distribution, n = 15, p = 0.25"}]
[2,"Each trial only results in S or F",null,null,"Yes",null,{"$f":"\"Random Discrete Variable = x = Stuck In Traffic in \"&E9&\" Tries\"","v":"Random Discrete Variable = x = Stuck In Traffic in 15 Tries"}]
[3,"p remains the same for each trial",null,null,"Yes"]
[4,"All events are independent",null,null,"Yes"]
[]
["n = # of Fixed Trials = # drive on bridge",null,null,null,15]
["p = Prob of Success =",null,null,null,0.25]
["X - Lower",null,null,null,2]
["X - Upper",null,null,null,5]
[null,null,null,null,{"$f":"_xlfn.BINOM.DIST(E12,E9,E10,1)-_xlfn.BINOM.DIST(E11-1,E9,E10,1)","v":0.77145115658640862}]
[]
["X","P(x) = f(x)",{"$f":"\"P(\"&E11&\"<=X<=\"&E12&\") = \"&ROUND(E13,4)","v":"P(2<=X<=5) = 0.7715"}]
[0,{"$f":"_xlfn.BINOM.DIST.RANGE(E9,E10,A16:A31)","v":1.3363461010158065E-2},{"$f":"IF((A16:A31>=E11)*(A16:A31<=E12),_xlfn.ANCHORARRAY(B16),\"\")","v":""}]
[1,6.6817305050790338E-2,""]
[2,0.15590704511851075,0.15590704511851075]
[3,0.22519906517118218,0.22519906517118218]
[4,0.22519906517118218,0.22519906517118218]
[5,0.16514598112553358,0.16514598112553358]
[6,9.1747767291963059E-2,""]
[7,3.9320471696555608E-2,""]
[8,1.3106823898851871E-2,""]
[9,3.398065455257893E-3,""]
[10,6.7961309105157863E-4,""]
[11,1.0297168046236046E-4,""]
[12,1.1441297829151157E-5,""]
[13,8.8009983301163059E-7,""]
[14,4.1909515857696467E-8,""]
[15,9.3132257461547934E-10,""]
["Total",{"$f":"SUM(B16:B31)","v":1}]

{"sheet":"Poisson Pattern Positive Skew","index":39,"n_rows":64,"n_cols":9,"rows_kept":64,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute",null,null,null,"Chart Title:",{"$f":"\"Poisson Distribution \"&B3&\" = \"&C3","v":"Poisson Distribution Expected Value = µ = = 5"}]
[null,"Expected Value = µ =",5,"people arriving/minute"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Self Spilling Report:"]
[]
[null,{"$f":"_xlfn.LET(\n_xlpm.mean,C3,\n_xlpm.seq,_xlfn.SEQUENCE(1000,,0),\n_xlpm.PP,_xlfn.POISSON.DIST(_xlpm.seq,_xlpm.mean,0),\n_xlpm.runPP,_xlfn.SCAN(0,_xlpm.PP,_xlfn.LAMBDA(_xlpm.a,_xlpm.r,_xlpm.a+_xlpm.r)),\n_xlpm.x,_xlfn.XLOOKUP(1,_xlpm.runPP,_xlpm.seq,,-1)+1,\n_xlpm.seqx,_xlfn.SEQUENCE(_xlpm.x,,0),\n_xlpm.PPx,_xlfn.POISSON.DIST(_xlpm.seqx,_xlpm.mean,0),\n_xlpm.r,_xlfn.VSTACK(_xlfn.HSTACK(\"X\",\"P(X)\"),_xlfn.HSTACK(_xlpm.seqx,_xlpm.PPx),_xlfn.HSTACK(\"Total\",SUM(_xlpm.PPx))),\n_xlpm.r)","v":"X"},"P(X)",null,"P(X)",null,null,"X"]
[null,0,6.737946999085467E-3,null,{"$f":"_xlfn.DROP(_xlfn.DROP(_xlfn.ANCHORARRAY(B29),-1,1),1)","v":6.737946999085467E-3},{"$f":"INDEX(_xlfn.ANCHORARRAY(B29),_xlfn.SEQUENCE(ROWS(_xlfn.ANCHORARRAY(B29))-2,,2),2)","v":6.737946999085467E-3},{"$f":"_xlfn.DROP(_xlfn.DROP(_xlfn.CHOOSECOLS(_xlfn.ANCHORARRAY(B29),2),-1),1)","v":6.737946999085467E-3},{"$f":"_xlfn.DROP(_xlfn.DROP(_xlfn.ANCHORARRAY(B29),-1,-1),1)","v":0}]
[null,1,3.368973499542733E-2,null,3.368973499542733E-2,3.368973499542733E-2,3.368973499542733E-2,1]
[null,2,8.4224337488568335E-2,null,8.4224337488568335E-2,8.4224337488568335E-2,8.4224337488568335E-2,2]
[null,3,0.14037389581428059,null,0.14037389581428059,0.14037389581428059,0.14037389581428059,3]
[null,4,0.17546736976785074,null,0.17546736976785074,0.17546736976785074,0.17546736976785074,4]
[null,5,0.17546736976785071,null,0.17546736976785071,0.17546736976785071,0.17546736976785071,5]
[null,6,0.14622280813987559,null,0.14622280813987559,0.14622280813987559,0.14622280813987559,6]
[null,7,0.104444862957054,null,0.104444862957054,0.104444862957054,0.104444862957054,7]
[null,8,6.5278039348158706E-2,null,6.5278039348158706E-2,6.5278039348158706E-2,6.5278039348158706E-2,8]
[null,9,3.6265577415643749E-2,null,3.6265577415643749E-2,3.6265577415643749E-2,3.6265577415643749E-2,9]
[null,10,1.8132788707821874E-2,null,1.8132788707821874E-2,1.8132788707821874E-2,1.8132788707821874E-2,10]
[null,11,8.2421766853735742E-3,null,8.2421766853735742E-3,8.2421766853735742E-3,8.2421766853735742E-3,11]
[null,12,3.4342402855723282E-3,null,3.4342402855723282E-3,3.4342402855723282E-3,3.4342402855723282E-3,12]
[null,13,1.3208616482970471E-3,null,1.3208616482970471E-3,1.3208616482970471E-3,1.3208616482970471E-3,13]
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[null,30,2.3657434461796165E-14,null,2.3657434461796165E-14,2.3657434461796165E-14,2.3657434461796165E-14,30]
[null,31,3.8157152357735622E-15,null,3.8157152357735622E-15,3.8157152357735622E-15,3.8157152357735622E-15,31]
[null,32,5.9620550558961939E-16,null,5.9620550558961939E-16,5.9620550558961939E-16,5.9620550558961939E-16,32]
[null,33,9.0334167513579496E-17,null,9.0334167513579496E-17,9.0334167513579496E-17,9.0334167513579496E-17,33]
[null,"Total",0.99999999999999989]

{"sheet":"Dick's","index":40,"n_rows":1317,"n_cols":15,"rows_kept":1317,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Data collected: Number of Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period.",null,null,null,null,null,null,null,null,null,null,null,"<=Raw Data Chart Title"]
[null,"Discrete Variable = X = Number of Arrivals in 1 min period during Sat. noon lunch rush (noon to 1 PM)"]
[]
[null,"Properties (Requirements) of a Poisson Experiment:",null,null,null,null,null,null,null,null,null,null,null,"POISSON Chart Title:"]
[null,"1) The probability of an occurrence (success) is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"]
[null,"2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
[null,"3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, mean doubles)."]
[null,"4) Mean = Variance (observed from calculations made off of source data)"]
[null,"5) As with all our distributions, actual Relative Frequency Pattern from past data must fit the pattern of the distribution you want to use, in our case the \"Poisson Pattern\""]
[]
[null,"X = Arrivals During 1 min",null,"X = Arrivals During 1 min","Frequency","P(X) Relative Frequency",null,"Mean",{"$f":"SUMPRODUCT(D13:D27,_xlfn.ANCHORARRAY(F13))","v":3.8796934865900377},null,"X = Arrivals During 1 min","P(X) POISSON Function",null,"Mean"]
[null,0,null,{"$f":"_xlfn.SEQUENCE(E33+1,,0)","v":0},{"$f":"COUNTIFS(B13:B1317,_xlfn.ANCHORARRAY(D13))","v":28},{"$f":"_xlfn.ANCHORARRAY(E13)/E28","v":2.1455938697318006E-2},null,"Variance",{"$f":"SUMPRODUCT((D13:D27-I12)^2,_xlfn.ANCHORARRAY(F13))","v":3.7518098677353535},null,{"$f":"_xlfn.SEQUENCE(O14+1,,0)","v":0},null,null,"Variance"]
[null,0,null,1,102,7.8160919540229884E-2,null,"SD",{"$f":"SQRT(I13)","v":1.9369589225730508},null,1,null,null,"Last X",29]
[null,0,null,2,191,0.14636015325670498,null,null,null,null,2]
[null,0,null,3,263,0.20153256704980843,null,null,null,null,3]
[null,0,null,4,266,0.20383141762452106,null,null,null,null,4]
[null,0,null,5,204,0.15632183908045977,null,null,null,null,5]
[null,0,null,6,136,0.10421455938697317,null,null,null,null,6]
[null,0,null,7,70,5.3639846743295021E-2,null,null,null,null,7]
[null,0,null,8,22,1.6858237547892719E-2,null,null,null,null,8]
[null,0,null,9,14,1.0727969348659003E-2,null,null,null,null,9]
[null,0,null,10,5,3.8314176245210726E-3,null,null,null,null,10]
[null,0,null,11,2,1.5325670498084292E-3,null,null,null,null,11]
[null,0,null,12,1,7.6628352490421458E-4,null,null,null,null,12]
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[null,0,null,14,1,7.6628352490421458E-4,null,null,null,null,14]
[null,0,null,"Total",{"$f":"SUM(_xlfn.ANCHORARRAY(E13))","v":1305},{"$f":"SUM(_xlfn.ANCHORARRAY(F13))","v":1},null,null,null,null,15]
[null,0,null,null,null,null,null,null,null,null,16]
[null,0,null,null,null,null,null,null,null,null,17]
[null,0,null,null,null,null,null,null,null,null,18]
[null,0,null,null,null,null,null,null,null,null,19]
[null,0,null,"Max Rooms",{"$f":"MAX(B13:B1317)","v":14},null,null,null,null,null,20]
[null,0,null,null,null,null,null,null,null,null,21]
[null,0,null,null,null,null,null,null,null,null,22]
[null,0,null,null,null,null,null,null,null,null,23]
[null,0,null,null,null,null,null,null,null,null,24]
[null,0,null,null,null,null,null,null,null,null,25]
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[null,0,null,null,null,null,null,null,null,null,27]
[null,1,null,null,null,null,null,null,null,null,28]
[null,1,null,null,null,null,null,null,null,null,29]
[null,1,null,null,null,null,null,null,null,null,"Total"]
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{"sheet":"Dick's (an)","index":41,"n_rows":1317,"n_cols":15,"rows_kept":1317,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Data collected: Number of Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period.",null,null,null,null,null,null,null,null,null,null,null,"<=Raw Data Chart Title"]
[null,"Discrete Variable = X = Number of Arrivals in 1 min period during Sat. noon lunch rush (noon to 1 PM)"]
[]
[null,"Properties (Requirements) of a Poisson Experiment:",null,null,null,null,null,null,null,null,null,null,null,"POISSON Chart Title:"]
[null,"1) The probability of an occurrence (success) is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"]
[null,"2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
[null,"3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, mean doubles)."]
[null,"4) Mean = Variance (observed from calculations made off of source data)"]
[null,"5) As with all our distributions, actual Relative Frequency Pattern from past data must fit the pattern of the distribution you want to use, in our case the \"Poisson Pattern\""]
[]
[null,"X = Arrivals During 1 min",null,"X = Arrivals During 1 min","Frequency","P(X) Relative Frequency",null,"Mean",{"$f":"SUMPRODUCT(D13:D27,_xlfn.ANCHORARRAY(F13))","v":3.8796934865900377},null,"X = Arrivals During 1 min","P(X) POISSON Function",null,"Mean",{"$f":"SUMPRODUCT(_xlfn.ANCHORARRAY(K13),_xlfn.ANCHORARRAY(L13))","v":3.8796934865900377}]
[null,0,null,{"$f":"_xlfn.SEQUENCE(E33+1,,0)","v":0},{"$f":"COUNTIFS(B13:B1317,_xlfn.ANCHORARRAY(D13))","v":28},{"$f":"_xlfn.ANCHORARRAY(E13)/E28","v":2.1455938697318006E-2},null,"Variance",{"$f":"SUMPRODUCT((D13:D27-I12)^2,_xlfn.ANCHORARRAY(F13))","v":3.7518098677353535},null,{"$f":"_xlfn.SEQUENCE(O14+1,,0)","v":0},{"$f":"_xlfn.POISSON.DIST(_xlfn.ANCHORARRAY(K13),I12,0)","v":2.0657155906734039E-2},null,"Variance",{"$f":"SUMPRODUCT((_xlfn.ANCHORARRAY(K13)-O12)^2,_xlfn.ANCHORARRAY(L13))","v":3.8796934865900115}]
[null,0,null,1,102,7.8160919540229884E-2,null,"SD",{"$f":"SQRT(I13)","v":1.9369589225730508},null,1,8.0143433222830962E-2,null,"Last X",29]
[null,0,null,2,191,0.14636015325670498,null,null,null,null,2,0.15546597793379047]
[null,0,null,3,263,0.20153256704980843,null,null,null,null,3,0.20105344732535915]
[null,0,null,4,266,0.20383141762452106,null,null,null,null,4,0.19500643751116731]
[null,0,null,5,204,0.15632183908045977,null,null,null,null,5,0.15131304109104057]
[null,0,null,6,136,0.10421455938697317,null,null,null,null,6,9.7841369992840196E-2]
[null,0,null,7,70,5.3639846743295021E-2,null,null,null,null,7,5.422778941146681E-2]
[null,0,null,8,22,1.6858237547892719E-2,null,null,null,null,8,2.629840017148051E-2]
[null,0,null,9,14,1.0727969348659003E-2,null,null,null,null,9,1.1336636872559043E-2]
[null,0,null,10,5,3.8314176245210726E-3,null,null,null,null,10,4.3982676234303724E-3]
[null,0,null,11,2,1.5325670498084292E-3,null,null,null,null,11,1.5512663864456972E-3]
[null,0,null,12,1,7.6628352490421458E-4,null,null,null,null,12,5.0153650795495405E-4]
[null,0,null,13,0,0,null,null,null,null,13,1.4967753255384184E-4]
[null,0,null,14,1,7.6628352490421458E-4,null,null,null,null,14,4.1478782009857794E-5]
[null,0,null,"Total",{"$f":"SUM(_xlfn.ANCHORARRAY(E13))","v":1305},{"$f":"SUM(_xlfn.ANCHORARRAY(F13))","v":1},null,null,null,null,15,1.0728330693022219E-5]
[null,0,null,null,null,null,null,null,null,null,16,2.6014146694813857E-6]
[null,0,null,null,null,null,null,null,null,null,17,5.9368773818274939E-7]
[null,0,null,null,null,null,null,null,null,null,18,1.279625806053326E-7]
[null,0,null,null,null,null,null,null,null,null,19,2.6129241605355779E-8]
[null,0,null,"Max Rooms",{"$f":"MAX(B13:B1317)","v":14},null,null,null,null,null,20,5.0686724232918323E-9]
[null,0,null,null,null,null,null,null,null,null,21,9.3642358982398654E-10]
[null,0,null,null,null,null,null,null,null,null,22,1.6513802282406363E-10]
[null,0,null,null,null,null,null,null,null,null,23,2.7855865719081618E-11]
[null,0,null,null,null,null,null,null,null,null,24,4.503009199735325E-12]
[null,0,null,null,null,null,null,null,null,null,25,6.9881181849072024E-13]
[null,0,null,null,null,null,null,null,null,null,26,1.0427598694425402E-13]
[null,0,null,null,null,null,null,null,null,null,27,1.4983661753902525E-14]
[null,1,null,null,null,null,null,null,null,null,28,2.0761433897101461E-15]
[null,1,null,null,null,null,null,null,null,null,29,2.7775172366501524E-16]
[null,1,null,null,null,null,null,null,null,null,"Total"]
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{"sheet":"POISSON.DIST","index":42,"n_rows":528,"n_cols":55,"rows_kept":528,"cut":false,"hidden":false,"merged":[]}
[]
[null,"POISSON Discrete Probability Distribution"]
[null,"Used to estimate the number of occurrences (successes) over specified interval of time or space"]
[null,"Whereas Binomial Experiment counts number of successes over a specified number of trials,"]
[null,"Poisson Experiment counts number of occurrences (successes) over specified  interval of time or space",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bell Normal Probability Distribution Curve Height Formula:"]
[null,"Good for estimating the probabilities of:"]
[null,"1) Line waiting situations, where you know the mean number of arrivals over a certain time interval"]
[null,"Example: From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute."]
[null,"With this information we can make estimates of the probability that a certain number of people will show up over this interval"]
[null,"2) Distance of road or pipe intervals, where you know the mean number of repairs over a certain distance interval"]
[null,{"$f":"\"Example: From past data we know that the mean number of water line breaks is \"&C95&\" per 100 miles of pipe in Richmond, CA.\"","v":"Example: From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."}]
[null,"With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Continuous Compounding Formula in Finance:"]
[null,"THE most amazing thing about this distribution is that the only number you need to make your probability calculations is the mean."]
[null,"Properties (Requirements) of a Poisson Experiment:"]
[null,"1) The probability of an occurrence (success) is the same for all equal-size intervals"]
[null,"2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
[null,"3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, mean doubles)."]
[null,"4) Mean = Variance (observed from calculations made off of source data)"]
[null,"5) As with all our distributions, actual Relative Frequency Pattern from past data must fit the pattern of the distribution you want to use, in our case the \"Poisson Pattern\""]
[null,"f(x) = P(x) = the probability of x occurrences in an interval = height of column when you plot column chart."]
[null,"Discrete Random Variable = X = Number of occurrences over a specified interval of time or space."]
[null,"No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gets quite small."]
[null,"Mean = µ = Calculated from past data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute"]
[null,"e = constant = 2.71828 = =EXP(1) in Excel",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"e",{"$f":"EXP(1)","v":2.7182818284590451},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(AA24:AA25),\"\")","v":"=EXP(1)"},null,"Series",null,"Number",null,null,null,null,null,null,null,null,null,null,null,"Expected Value = µ =",3.88,"people arriving/minute"]
[null,"In Excel use: POISSON.DIST(x,mean,cumulative)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"e",{"$f":"SUM(1/FACT(_xlfn.SEQUENCE(AG25,,0)))","v":2.7182815255731922},null,"=SUM(1/FACT(SEQUENCE(AG25,,0)))",null,{"$f":"1/FACT(_xlfn.SEQUENCE(AG25,,0))","v":1},null,10]
[null,"x = Number of occurrences over a specified interval of time or space = Discrete Random Variable",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,"Last X",500]
[null,"mean = µ = Calculated from past data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Self Spilling Report:"]
[null,"cumulative = 0 for exactly x OR 1 for less than or equal to x",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16666666666666666,null,null,null,null,null,null,null,null,null,null,null,null,null,"X","P(X)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.1666666666666664E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.SEQUENCE(AT26,,0)","v":0},{"$f":"_xlfn.POISSON.DIST(_xlfn.ANCHORARRAY(AS29),AT24,0)","v":2.0650825181712566E-2},null,{"$f":"AT29","v":2.0650825181712566E-2},null,{"$f":"_xlfn.LET(\n_xlpm.mean,AT24,\n_xlpm.seq,_xlfn.SEQUENCE(1000,,0),\n_xlpm.PP,_xlfn.POISSON.DIST(_xlpm.seq,_xlpm.mean,0),\n_xlpm.runPP,_xlfn.SCAN(0,_xlpm.PP,_xlfn.LAMBDA(_xlpm.a,_xlpm.r,_xlpm.a+_xlpm.r)),\n_xlpm.x,_xlfn.XLOOKUP(1,_xlpm.runPP,_xlpm.seq,,-1)+1,\n_xlpm.seqx,_xlfn.SEQUENCE(_xlpm.x,,0),\n_xlpm.PPx,_xlfn.POISSON.DIST(_xlpm.seqx,_xlpm.mean,0),\n_xlpm.r,_xlfn.VSTACK(_xlfn.HSTACK(\"X\",\"P(X)\"),_xlfn.HSTACK(_xlpm.seqx,_xlpm.PPx),_xlfn.HSTACK(\"Total\",SUM(_xlpm.PPx))),\n_xlpm.r)","v":"X"},"P(X)",null,{"$f":"_xlfn.DROP(_xlfn.DROP(_xlfn.ANCHORARRAY(AX29),-1,1),1)","v":2.0650825181712566E-2},{"$f":"INDEX(_xlfn.ANCHORARRAY(AX29),_xlfn.SEQUENCE(ROWS(_xlfn.ANCHORARRAY(AX29))-2,,2),2)","v":2.0650825181712566E-2},{"$f":"_xlfn.DROP(_xlfn.DROP(_xlfn.CHOOSECOLS(_xlfn.ANCHORARRAY(AX29),2),-1),1)","v":2.0650825181712566E-2}]
[null,"Example 1:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.3333333333333332E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,1,8.0125201705044752E-2,null,{"$f":"AV29+AT30","v":0.10077602688675733},null,0,2.0650825181712566E-2,null,8.0125201705044752E-2,8.0125201705044752E-2,8.0125201705044752E-2]
[null,"From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute.",null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.3888888888888889E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,2,0.1554428913077868,null,{"$f":"AV30+AT31","v":0.25621891819454412},null,1,8.0125201705044752E-2,null,0.1554428913077868,0.1554428913077868,0.1554428913077868]
[null,"Assume:  The probability of a person arriving is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.9841269841269841E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,3,0.20103947275807099,null,0.45725839095261511,null,2,0.1554428913077868,null,0.20103947275807099,0.20103947275807099,0.20103947275807099]
[null,"Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4801587301587302E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,4,0.19500828857532884,null,0.65226667952794393,null,3,0.20103947275807099,null,0.19500828857532884,0.19500828857532884,0.19500828857532884]
[null,"Goal: calculate the probability that 0 people will arrive in 1 minute. 3 to 5 people in 1 minute?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7557319223985893E-6,null,null,null,null,null,null,null,null,null,null,null,null,null,5,0.15132643193445516,null,0.80359311146239909,null,4,0.19500828857532884,null,0.15132643193445516,0.15132643193445516,0.15132643193445516]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,9.7857759317614312E-2,null,0.9014508707800134,null,5,0.15132643193445516,null,9.7857759317614312E-2,9.7857759317614312E-2,9.7857759317614312E-2]
[null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute",null,null,null,null,"Last X",30,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7,5.4241158021763422E-2,null,0.95569202880177684,null,6,9.7857759317614312E-2,null,5.4241158021763422E-2,5.4241158021763422E-2,5.4241158021763422E-2]
[null,"Expected Value = µ =",3.88,"people arriving/minute",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,2.6306961640555224E-2,null,0.98199899044233208,null,7,5.4241158021763422E-2,null,2.6306961640555224E-2,2.6306961640555224E-2,2.6306961640555224E-2]
[null,"X",0,null,null,null,null,null,"X","P(x)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9,1.134122346281714E-2,null,0.99334021390514926,null,8,2.6306961640555224E-2,null,1.134122346281714E-2,1.134122346281714E-2,1.134122346281714E-2]
[null,{"$f":"\"P(\"&C38&\")\"","v":"P(0)"},null,null,{"$f":"C37^C38*EXP(1)^-C37/FACT(C38)","v":2.0650825181712566E-2},null,null,null,{"$f":"_xlfn.SEQUENCE(J36+1,,0)","v":0},{"$f":"_xlfn.POISSON.DIST(I39:I69,C37,0)","v":2.0650825181712566E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10,4.400394703573055E-3,null,0.99774060860872227,null,9,1.134122346281714E-2,null,4.400394703573055E-3,4.400394703573055E-3,4.400394703573055E-3]
[null,"X",3,null,null,null,null,null,1,8.0125201705044752E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,11,1.5521392227148608E-3,null,0.99929274783143718,null,10,4.400394703573055E-3,null,1.5521392227148608E-3,1.5521392227148608E-3,1.5521392227148608E-3]
[null,"X",5,null,null,null,null,null,2,0.1554428913077868,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12,5.0185834867780407E-4,null,0.99979460618011495,null,11,1.5521392227148608E-3,null,5.0185834867780407E-4,5.0185834867780407E-4,5.0185834867780407E-4]
[null,{"$f":"\"P(\"&$C$40&\"<= Arrivals in 1 minute  <=\"&$C$41&\")\"","v":"P(3<= Arrivals in 1 minute  <=5)"},null,null,{"$f":"SUM(_xlfn.POISSON.DIST(_xlfn.SEQUENCE(C41-C40+1,,C40),C37,0))","v":0.54737419326785497},null,null,null,3,0.20103947275807099,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,13,1.4978541483614462E-4,null,0.99994439159495108,null,12,5.0185834867780407E-4,null,1.4978541483614462E-4,1.4978541483614462E-4,1.4978541483614462E-4]
[null,"Expected Value = µ =",null,0.5,"minutes",null,null,null,4,0.19500828857532884,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,14,4.1511957826017288E-5,null,0.99998590355277706,null,13,1.4978541483614462E-4,null,4.1511957826017288E-5,4.1511957826017288E-5,4.1511957826017288E-5]
[null,"X",2,null,null,null,null,null,5,0.15132643193445516,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,15,1.0737759757663123E-5,null,0.99999664131253474,null,14,4.1511957826017288E-5,null,1.0737759757663123E-5,1.0737759757663123E-5,1.0737759757663123E-5]
[null,{"$f":"\"P(\"&C44&\" Arrivals in \"&TEXT(D43,\"?/?\")&\" min)\"","v":"P(2 Arrivals in 1/2 min)"},null,null,{"$f":"C43^C44*EXP(1)^-C43/FACT(C44)","v":0},null,null,null,6,9.7857759317614312E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,16,2.6039067412333054E-6,null,0.99999924521927597,null,15,1.0737759757663123E-5,null,2.6039067412333054E-6,2.6039067412333054E-6,2.6039067412333054E-6]
[null,null,null,null,null,null,null,null,7,5.4241158021763422E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,17,5.943034209403063E-7,null,0.99999983952269689,null,16,2.6039067412333054E-6,null,5.943034209403063E-7,5.943034209403063E-7,5.943034209403063E-7]
[null,null,null,null,null,null,null,null,8,2.6306961640555224E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,18,1.2810540406935535E-7,null,0.99999996762810095,null,17,5.943034209403063E-7,null,1.2810540406935535E-7,1.2810540406935535E-7,1.2810540406935535E-7]
[null,null,null,null,null,null,null,null,9,1.134122346281714E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19,2.61604719888999E-8,null,0.99999999378857296,null,18,1.2810540406935535E-7,null,2.61604719888999E-8,2.61604719888999E-8,2.61604719888999E-8]
[null,null,null,null,null,null,null,null,10,4.400394703573055E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,5.0751315658465849E-9,null,0.9999999988637045,null,19,2.61604719888999E-8,null,5.0751315658465849E-9,5.0751315658465849E-9,5.0751315658465849E-9]
[null,null,null,null,null,null,null,null,11,1.5521392227148608E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21,9.3769097502308185E-10,null,0.99999999980139542,null,20,5.0751315658465849E-9,null,9.3769097502308185E-10,9.3769097502308185E-10,9.3769097502308185E-10]
[null,null,null,null,null,null,null,null,12,5.0185834867780407E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,22,1.6537459014043502E-10,null,0.99999999996677003,null,21,9.3769097502308185E-10,null,1.6537459014043502E-10,1.6537459014043502E-10,1.6537459014043502E-10]
[null,null,null,null,null,null,null,null,13,1.4978541483614462E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,23,2.7897974336734243E-11,null,0.99999999999466804,null,22,1.6537459014043502E-10,null,2.7897974336734243E-11,2.7897974336734243E-11,2.7897974336734243E-11]
[null,null,null,null,null,null,null,null,14,4.1511957826017288E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,24,4.5101725177720354E-12,null,0.99999999999917821,null,23,2.7897974336734243E-11,null,4.5101725177720354E-12,4.5101725177720354E-12,4.5101725177720354E-12]
[null,null,null,null,null,null,null,null,15,1.0737759757663123E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,25,6.9997877475821791E-13,null,0.99999999999987821,null,24,4.5101725177720354E-12,null,6.9997877475821791E-13,6.9997877475821791E-13,6.9997877475821791E-13]
[null,null,null,null,null,null,null,null,16,2.6039067412333054E-6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,26,1.0445837100238E-13,null,0.99999999999998268,null,25,6.9997877475821791E-13,null,1.0445837100238E-13,1.0445837100238E-13,1.0445837100238E-13]
[null,null,null,null,null,null,null,null,17,5.943034209403063E-7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,27,1.5011054795897582E-14,null,0.99999999999999767,null,26,1.0445837100238E-13,null,1.5011054795897582E-14,1.5011054795897582E-14,1.5011054795897582E-14]
[null,null,null,null,null,null,null,null,18,1.2810540406935535E-7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,28,2.0801033074315417E-15,null,0.99999999999999978,null,27,1.5011054795897582E-14,null,2.0801033074315417E-15,2.0801033074315417E-15,2.0801033074315417E-15]
[null,null,null,null,null,null,null,null,19,2.61604719888999E-8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,29,2.7830347699428757E-16,null,1,null,28,2.0801033074315417E-15,null,2.7830347699428757E-16,2.7830347699428757E-16,2.7830347699428757E-16]
[null,null,null,null,null,null,null,null,20,5.0751315658465849E-9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,30,3.599391635792812E-17,null,1,null,29,2.7830347699428757E-16]
[null,null,null,null,null,null,null,null,21,9.3769097502308185E-10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,31,4.505045015121321E-18,null,1,null,"Total",1]
[null,null,null,null,null,null,null,null,22,1.6537459014043502E-10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,32,5.4623670808345393E-19,null,1]
[null,null,null,null,null,null,null,null,23,2.7897974336734243E-11,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,33,6.4224194768600517E-20,null,1]
[null,null,null,null,null,null,null,null,24,4.5101725177720354E-12,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,34,7.3291139912402643E-21,null,1]
[null,null,null,null,null,null,null,null,25,6.9997877475821791E-13,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,35,8.1248463674320684E-22,null,1]
[null,null,null,null,null,null,null,null,26,1.0445837100238E-13,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,36,8.7567788626766887E-23,null,1]
[null,null,null,null,null,null,null,null,27,1.5011054795897582E-14,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,37,9.182784320860972E-24,null,1]
[null,null,null,null,null,null,null,null,28,2.0801033074315417E-15,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,38,9.3761060960370192E-25,null,1]
[null,null,null,null,null,null,null,null,29,2.7830347699428757E-16,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,39,9.3280235006726712E-26,null,1]
[null,null,null,null,null,null,null,null,30,3.599391635792812E-17,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,40,9.0481827956525115E-27,null,1]
[null,null,null,null,null,null,null,null,null,{"$f":"SUM(J39:J69)","v":1},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,41,8.5626705480809776E-28,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,42,7.9102766015605244E-29,null,1]
[null,"Example 2:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,43,7.1376449335011312E-30,null,1]
[null,"From past data we know that the mean number of arrivals for accounting tutoring is 3 per hour during the morning shift",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,44,6.2941050777236731E-31,null,1]
[null,"Assume:  The probability of a person arriving is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,45,5.4269172670151345E-32,null,1]
[null,"Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,46,4.5774867382649625E-33,null,1]
[null,"Goal: calculate the probability that 5 people will arrive in 1 hour",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,47,3.7788613924399388E-34,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,48,3.0545796255556513E-35,null,1]
[null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 hour",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,49,2.4187283565624095E-36,null,1]
[null,"Expected Value = µ =",3,"people arriving/hour",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,50,1.8769332046924351E-37,null,1]
[null,"X",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,51,1.4279413400405362E-38,null,1]
[null,{"$f":"\"P(\"&C80&\")\"","v":"P(5)"},null,null,{"$f":"(C79^C80*EXP(1)^-C79)/FACT(C80)","v":0.10081881344492451},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,52,1.0654639229533116E-39,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,53,7.8000000397337777E-41,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,54,5.604444472993896E-42,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,55,3.9536808282211412E-43,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,56,2.7393360024102909E-44,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,57,1.8646708226933837E-45,null,1]
[null,"Example 3:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,58,1.2474004813879929E-46,null,1]
[null,{"$f":"\"From past data we know that the mean number of water line breaks is \"&C95&\" per 100 miles of pipe in Richmond, CA.\"","v":"From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,59,8.2032438437038911E-48,null,1]
[null,"With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch in Richmond, CA.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,60,5.304764352262018E-49,null,1]
[null,"Assume:  The probability of a water breaks is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,61,3.3741779814387374E-50,null,1]
[null,"Assume: The number of water breaks in any interval is independent of the number of water breaks in any other interval",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,62,2.1115823496745902E-51,null,1]
[null,{"$f":"\"Goal: calculate the probability that \"&C96&\" or more breaks will occur over a 100 mile stretch of pipe.\"","v":"Goal: calculate the probability that 30 or more breaks will occur over a 100 mile stretch of pipe."},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,63,1.3004665899582873E-52,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,64,7.884078701622293E-54,null,1]
[null,"Define Random Discrete Variable = x = ",null,"x = Number of water breaks in 100 miles of pipe",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,65,4.7061885172760343E-55,null,1]
[null,"Expected Value = µ =",25,"water breaks/100 miles",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,66,2.7666684010653435E-56,null,{"$f":"AV94+AT95","v":1}]
[null,"X",30,null,null,null,"Last X",74,null,null,null,null,null,null,{"$f":"\"Mean number of water line breaks is \"&C95&\" per 100 miles of pipe in Richmond, CA.\"","v":"Mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,67,1.6021900591244016E-57,null,1]
[null,{"$f":"\"P(x>=\"&$C$96&\")\"","v":"P(x>=30)"},null,null,{"$f":"SUM(_xlfn.POISSON.DIST(_xlfn.SEQUENCE(H96-C96,,C96),C95,0))","v":0.1821039159774534},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,68,9.1419079844156121E-59,null,1]
[null,{"$f":"\"P(x>=\"&$C$96&\")\"","v":"P(x>=30)"},null,null,{"$f":"SUMIFS(_xlfn.ANCHORARRAY(C105),B105:B179,\">=\"&C96)","v":0.18210391597745457},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,69,5.1406670984829612E-60,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,70,2.8493983345877371E-61,null,1]
[null,"X",10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,71,1.5571359912958647E-62,null,1]
[null,{"$f":"\"P(x<\"&$C$100&\")\"","v":"P(x<10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,72,8.3912328419828366E-64,null,1]
[null,{"$f":"\"P(x<\"&$C$100&\")\"","v":"P(x<10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,73,4.4599977297115059E-65,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,74,2.3384852961190785E-66,null,1]
[null,"X","P(x)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,75,1.2097763931922681E-67,null,1]
[null,{"$f":"_xlfn.SEQUENCE(H96+1,,0)","v":0},{"$f":"_xlfn.POISSON.DIST(B105:B179,C95,0)","v":1.3887943864964021E-11},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,76,6.1762268494548736E-69,null,1]
[null,1,3.4719859662410047E-10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,77,3.1121766462189314E-70,null,1]
[null,2,4.3399824578012608E-9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,78,1.5481083829909833E-71,null,1]
[null,3,3.6166520481677125E-8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,79,7.6033677544364016E-73,null,1]
[null,4,2.2604075301048233E-7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,80,3.6876333609017507E-74,null,1]
[null,5,1.1302037650524102E-6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,81,1.766421906209692E-75,null,1]
[null,6,4.7091823543850467E-6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,82,8.358191458650689E-77,null,1]
[null,7,1.6818508408517987E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,83,3.9072027541644905E-78,null,1]
[null,8,5.2557838776618804E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,84,1.8047555578759992E-79,null,1]
[null,9,1.4599399660171887E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,85,8.2381783112456254E-81,null,1]
[null,10,3.6498499150429664E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,86,3.7167595171666632E-82,null,1]
[null,11,8.29511344327948E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,87,1.6575893019087375E-83,null,1]
[null,12,1.7281486340165607E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,88,7.308461922052332E-85,null,1]
[null,13,3.3233627577241454E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,89,3.1861609278161988E-86,null,1]
[null,14,5.934576353078834E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,90,1.3735893777696171E-87,null,1]
[null,15,9.8909605884647447E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,91,5.856622841479459E-89,null,1]
[null,16,1.5454625919476139E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,92,2.4699670244499511E-90,null,1]
[null,17,2.2727391058053149E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,93,1.030480866114621E-91,null,1]
[null,18,3.1565820913962726E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,94,4.2534742133242029E-93,null,1]
[null,19,4.1533974886793022E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,95,1.7372084155470985E-94,null,1]
[null,20,5.1917468608491307E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,96,7.0212173461694197E-96,null,1]
[null,21,6.1806510248203946E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,97,2.808486938467832E-97,null,1]
[null,22,7.0234670736595409E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,98,1.1119315633934049E-98,null,1]
[null,23,7.6342033409342827E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,99,4.357873197945792E-100,null,1]
[null,24,7.9522951468065442E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,100,1.6908548008029224E-101,null,1]
[null,25,7.9522951468065442E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,101,6.4955610169460924E-103,null,1]
[null,26,7.6464376411601379E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,102,2.4708604652697445E-104,null,1]
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{"sheet":"POISSON.DIST (an)","index":43,"n_rows":528,"n_cols":55,"rows_kept":528,"cut":false,"hidden":false,"merged":[]}
[]
[null,"POISSON Discrete Probability Distribution"]
[null,"Used to estimate the number of occurrences (successes) over specified interval of time or space"]
[null,"Whereas Binomial Experiment counts number of successes over a specified number of trials,"]
[null,"Poisson Experiment counts number of occurrences (successes) over specified  interval of time or space",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bell Normal Probability Distribution Curve Height Formula:"]
[null,"Good for estimating the probabilities of:"]
[null,"1) Line waiting situations, where you know the mean number of arrivals over a certain time interval"]
[null,"Example: From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute."]
[null,"With this information we can make estimates of the probability that a certain number of people will show up over this interval"]
[null,"2) Distance of road or pipe intervals, where you know the mean number of repairs over a certain distance interval"]
[null,{"$f":"\"Example: From past data we know that the mean number of water line breaks is \"&C95&\" per 100 miles of pipe in Richmond, CA.\"","v":"Example: From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."}]
[null,"With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Continuous Compounding Formula in Finance:"]
[null,"THE most amazing thing about this distribution is that the only number you need to make your probability calculations is the mean."]
[null,"Properties (Requirements) of a Poisson Experiment:"]
[null,"1) The probability of an occurrence (success) is the same for all equal-size intervals"]
[null,"2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
[null,"3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, mean doubles)."]
[null,"4) Mean = Variance (observed from calculations made off of source data)"]
[null,"5) As with all our distributions, actual Relative Frequency Pattern from past data must fit the pattern of the distribution you want to use, in our case the \"Poisson Pattern\""]
[null,"f(x) = P(x) = the probability of x occurrences in an interval = height of column when you plot column chart."]
[null,"Discrete Random Variable = X = Number of occurrences over a specified interval of time or space."]
[null,"No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gets quite small."]
[null,"Mean = µ = Calculated from past data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute"]
[null,"e = constant = 2.71828 = =EXP(1) in Excel",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"e",{"$f":"EXP(1)","v":2.7182818284590451},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(AA24:AA25),\"\")","v":"=EXP(1)"},null,"Series",null,"Number",null,null,null,null,null,null,null,null,null,null,null,"Expected Value = µ =",3.88,"people arriving/minute"]
[null,"In Excel use: POISSON.DIST(x,mean,cumulative)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"e",{"$f":"SUM(1/FACT(_xlfn.SEQUENCE(AG25,,0)))","v":2.7182815255731922},null,"=SUM(1/FACT(SEQUENCE(AG25,,0)))",null,{"$f":"1/FACT(_xlfn.SEQUENCE(AG25,,0))","v":1},null,10]
[null,"x = Number of occurrences over a specified interval of time or space = Discrete Random Variable",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,"Last X",500]
[null,"mean = µ = Calculated from past data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Self Spilling Report:"]
[null,"cumulative = 0 for exactly x OR 1 for less than or equal to x",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16666666666666666,null,null,null,null,null,null,null,null,null,null,null,null,null,"X","P(X)"]
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[null,"Example 1:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8.3333333333333332E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,1,8.0125201705044752E-2,null,{"$f":"AV29+AT30","v":0.10077602688675733},null,0,2.0650825181712566E-2,null,8.0125201705044752E-2,8.0125201705044752E-2,8.0125201705044752E-2]
[null,"From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute.",null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.3888888888888889E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,2,0.1554428913077868,null,{"$f":"AV30+AT31","v":0.25621891819454412},null,1,8.0125201705044752E-2,null,0.1554428913077868,0.1554428913077868,0.1554428913077868]
[null,"Assume:  The probability of a person arriving is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.9841269841269841E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,3,0.20103947275807099,null,0.45725839095261511,null,2,0.1554428913077868,null,0.20103947275807099,0.20103947275807099,0.20103947275807099]
[null,"Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4801587301587302E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,4,0.19500828857532884,null,0.65226667952794393,null,3,0.20103947275807099,null,0.19500828857532884,0.19500828857532884,0.19500828857532884]
[null,"Goal: calculate the probability that 0 people will arrive in 1 minute. 3 to 5 people in 1 minute?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7557319223985893E-6,null,null,null,null,null,null,null,null,null,null,null,null,null,5,0.15132643193445516,null,0.80359311146239909,null,4,0.19500828857532884,null,0.15132643193445516,0.15132643193445516,0.15132643193445516]
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[null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute",null,null,null,null,"Last X",30,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7,5.4241158021763422E-2,null,0.95569202880177684,null,6,9.7857759317614312E-2,null,5.4241158021763422E-2,5.4241158021763422E-2,5.4241158021763422E-2]
[null,"Expected Value = µ =",3.88,"people arriving/minute",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,2.6306961640555224E-2,null,0.98199899044233208,null,7,5.4241158021763422E-2,null,2.6306961640555224E-2,2.6306961640555224E-2,2.6306961640555224E-2]
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[null,"X",3,null,null,null,null,null,1,8.0125201705044752E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,11,1.5521392227148608E-3,null,0.99929274783143718,null,10,4.400394703573055E-3,null,1.5521392227148608E-3,1.5521392227148608E-3,1.5521392227148608E-3]
[null,"X",5,null,null,null,null,null,2,0.1554428913077868,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,12,5.0185834867780407E-4,null,0.99979460618011495,null,11,1.5521392227148608E-3,null,5.0185834867780407E-4,5.0185834867780407E-4,5.0185834867780407E-4]
[null,{"$f":"\"P(\"&$C$40&\"<= Arrivals in 1 minute  <=\"&$C$41&\")\"","v":"P(3<= Arrivals in 1 minute  <=5)"},{"$f":"_xlfn.POISSON.DIST(C41,C37,1)-_xlfn.POISSON.DIST(C40-1,C37,1)","v":0.54737419326785508},null,{"$f":"SUM(_xlfn.POISSON.DIST(_xlfn.SEQUENCE(C41-C40+1,,C40),C37,0))","v":0.54737419326785497},null,null,null,3,0.20103947275807099,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,13,1.4978541483614462E-4,null,0.99994439159495108,null,12,5.0185834867780407E-4,null,1.4978541483614462E-4,1.4978541483614462E-4,1.4978541483614462E-4]
[null,"Expected Value = µ =",{"$f":"C37*D43","v":1.94},0.5,"minutes",null,null,null,4,0.19500828857532884,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,14,4.1511957826017288E-5,null,0.99998590355277706,null,13,1.4978541483614462E-4,null,4.1511957826017288E-5,4.1511957826017288E-5,4.1511957826017288E-5]
[null,"X",2,null,null,null,null,null,5,0.15132643193445516,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,15,1.0737759757663123E-5,null,0.99999664131253474,null,14,4.1511957826017288E-5,null,1.0737759757663123E-5,1.0737759757663123E-5,1.0737759757663123E-5]
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[null,null,null,null,null,null,null,null,10,4.400394703573055E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,20,5.0751315658465849E-9,null,0.9999999988637045,null,19,2.61604719888999E-8,null,5.0751315658465849E-9,5.0751315658465849E-9,5.0751315658465849E-9]
[null,null,null,null,null,null,null,null,11,1.5521392227148608E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,21,9.3769097502308185E-10,null,0.99999999980139542,null,20,5.0751315658465849E-9,null,9.3769097502308185E-10,9.3769097502308185E-10,9.3769097502308185E-10]
[null,null,null,null,null,null,null,null,12,5.0185834867780407E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,22,1.6537459014043502E-10,null,0.99999999996677003,null,21,9.3769097502308185E-10,null,1.6537459014043502E-10,1.6537459014043502E-10,1.6537459014043502E-10]
[null,null,null,null,null,null,null,null,13,1.4978541483614462E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,23,2.7897974336734243E-11,null,0.99999999999466804,null,22,1.6537459014043502E-10,null,2.7897974336734243E-11,2.7897974336734243E-11,2.7897974336734243E-11]
[null,null,null,null,null,null,null,null,14,4.1511957826017288E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,24,4.5101725177720354E-12,null,0.99999999999917821,null,23,2.7897974336734243E-11,null,4.5101725177720354E-12,4.5101725177720354E-12,4.5101725177720354E-12]
[null,null,null,null,null,null,null,null,15,1.0737759757663123E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,25,6.9997877475821791E-13,null,0.99999999999987821,null,24,4.5101725177720354E-12,null,6.9997877475821791E-13,6.9997877475821791E-13,6.9997877475821791E-13]
[null,null,null,null,null,null,null,null,16,2.6039067412333054E-6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,26,1.0445837100238E-13,null,0.99999999999998268,null,25,6.9997877475821791E-13,null,1.0445837100238E-13,1.0445837100238E-13,1.0445837100238E-13]
[null,null,null,null,null,null,null,null,17,5.943034209403063E-7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,27,1.5011054795897582E-14,null,0.99999999999999767,null,26,1.0445837100238E-13,null,1.5011054795897582E-14,1.5011054795897582E-14,1.5011054795897582E-14]
[null,null,null,null,null,null,null,null,18,1.2810540406935535E-7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,28,2.0801033074315417E-15,null,0.99999999999999978,null,27,1.5011054795897582E-14,null,2.0801033074315417E-15,2.0801033074315417E-15,2.0801033074315417E-15]
[null,null,null,null,null,null,null,null,19,2.61604719888999E-8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,29,2.7830347699428757E-16,null,1,null,28,2.0801033074315417E-15,null,2.7830347699428757E-16,2.7830347699428757E-16,2.7830347699428757E-16]
[null,null,null,null,null,null,null,null,20,5.0751315658465849E-9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,30,3.599391635792812E-17,null,1,null,29,2.7830347699428757E-16]
[null,null,null,null,null,null,null,null,21,9.3769097502308185E-10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,31,4.505045015121321E-18,null,1,null,"Total",1]
[null,null,null,null,null,null,null,null,22,1.6537459014043502E-10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,32,5.4623670808345393E-19,null,1]
[null,null,null,null,null,null,null,null,23,2.7897974336734243E-11,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,33,6.4224194768600517E-20,null,1]
[null,null,null,null,null,null,null,null,24,4.5101725177720354E-12,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,34,7.3291139912402643E-21,null,1]
[null,null,null,null,null,null,null,null,25,6.9997877475821791E-13,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,35,8.1248463674320684E-22,null,1]
[null,null,null,null,null,null,null,null,26,1.0445837100238E-13,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,36,8.7567788626766887E-23,null,1]
[null,null,null,null,null,null,null,null,27,1.5011054795897582E-14,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,37,9.182784320860972E-24,null,1]
[null,null,null,null,null,null,null,null,28,2.0801033074315417E-15,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,38,9.3761060960370192E-25,null,1]
[null,null,null,null,null,null,null,null,29,2.7830347699428757E-16,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,39,9.3280235006726712E-26,null,1]
[null,null,null,null,null,null,null,null,30,3.599391635792812E-17,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,40,9.0481827956525115E-27,null,1]
[null,null,null,null,null,null,null,null,null,{"$f":"SUM(J39:J69)","v":1},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,41,8.5626705480809776E-28,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,42,7.9102766015605244E-29,null,1]
[null,"Example 2:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,43,7.1376449335011312E-30,null,1]
[null,"From past data we know that the mean number of arrivals for accounting tutoring is 3 per hour during the morning shift",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,44,6.2941050777236731E-31,null,1]
[null,"Assume:  The probability of a person arriving is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,45,5.4269172670151345E-32,null,1]
[null,"Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,46,4.5774867382649625E-33,null,1]
[null,"Goal: calculate the probability that 5 people will arrive in 1 hour",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,47,3.7788613924399388E-34,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,48,3.0545796255556513E-35,null,1]
[null,"Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 hour",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,49,2.4187283565624095E-36,null,1]
[null,"Expected Value = µ =",3,"people arriving/hour",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,50,1.8769332046924351E-37,null,1]
[null,"X",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,51,1.4279413400405362E-38,null,1]
[null,{"$f":"\"P(\"&C80&\")\"","v":"P(5)"},{"$f":"_xlfn.POISSON.DIST(C80,C79,0)","v":0.10081881344492449},null,{"$f":"(C79^C80*EXP(1)^-C79)/FACT(C80)","v":0.10081881344492451},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,52,1.0654639229533116E-39,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,53,7.8000000397337777E-41,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,54,5.604444472993896E-42,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,55,3.9536808282211412E-43,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,56,2.7393360024102909E-44,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,57,1.8646708226933837E-45,null,1]
[null,"Example 3:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,58,1.2474004813879929E-46,null,1]
[null,{"$f":"\"From past data we know that the mean number of water line breaks is \"&C95&\" per 100 miles of pipe in Richmond, CA.\"","v":"From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,59,8.2032438437038911E-48,null,1]
[null,"With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch in Richmond, CA.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,60,5.304764352262018E-49,null,1]
[null,"Assume:  The probability of a water breaks is the same for all equal-size intervals",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,61,3.3741779814387374E-50,null,1]
[null,"Assume: The number of water breaks in any interval is independent of the number of water breaks in any other interval",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,62,2.1115823496745902E-51,null,1]
[null,{"$f":"\"Goal: calculate the probability that \"&C96&\" or more breaks will occur over a 100 mile stretch of pipe.\"","v":"Goal: calculate the probability that 30 or more breaks will occur over a 100 mile stretch of pipe."},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,63,1.3004665899582873E-52,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,64,7.884078701622293E-54,null,1]
[null,"Define Random Discrete Variable = x = ",null,"x = Number of water breaks in 100 miles of pipe",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,65,4.7061885172760343E-55,null,1]
[null,"Expected Value = µ =",25,"water breaks/100 miles",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,66,2.7666684010653435E-56,null,{"$f":"AV94+AT95","v":1}]
[null,"X",30,null,null,null,"Last X",74,null,null,null,null,null,null,{"$f":"\"Mean number of water line breaks is \"&C95&\" per 100 miles of pipe in Richmond, CA.\"","v":"Mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,67,1.6021900591244016E-57,null,1]
[null,{"$f":"\"P(x>=\"&$C$96&\")\"","v":"P(x>=30)"},{"$f":"1-_xlfn.POISSON.DIST(C96-1,C95,1)","v":0.18210391597745512},null,{"$f":"SUM(_xlfn.POISSON.DIST(_xlfn.SEQUENCE(H96-C96,,C96),C95,0))","v":0.1821039159774534},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,68,9.1419079844156121E-59,null,1]
[null,{"$f":"\"P(x>=\"&$C$96&\")\"","v":"P(x>=30)"},{"$f":"SUM(C135:C179)","v":0.18210391597745457},null,{"$f":"SUMIFS(_xlfn.ANCHORARRAY(C105),B105:B179,\">=\"&C96)","v":0.18210391597745457},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,69,5.1406670984829612E-60,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,70,2.8493983345877371E-61,null,1]
[null,"X",10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,71,1.5571359912958647E-62,null,1]
[null,{"$f":"\"P(x<\"&$C$100&\")\"","v":"P(x<10)"},{"$f":"_xlfn.POISSON.DIST(C100-1,C95,1)","v":2.2147663824878362E-4},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,72,8.3912328419828366E-64,null,1]
[null,{"$f":"\"P(x<\"&$C$100&\")\"","v":"P(x<10)"},{"$f":"SUM(C105:C114)","v":2.2147663824878357E-4},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,73,4.4599977297115059E-65,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,74,2.3384852961190785E-66,null,1]
[null,"X","P(x)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,75,1.2097763931922681E-67,null,1]
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{"sheet":"HYPGEOM.DIST","index":44,"n_rows":136,"n_cols":13,"rows_kept":136,"cut":false,"hidden":false,"merged":[[91,1,91,13]]}
[]
[null,"Example 1:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Goal: Calculate the probability that you can pull 2 straight Queens from a deck of cards (without replacement)?"]
[]
[null,"Experiment variables:"]
[null,"Population size = # of cards in deck = number_pop =",null,null,null,null,null,null,null,null,null,null,52]
[null,"Successes in population = # of Queen cards in population = population_s =",null,null,null,null,null,null,null,null,null,null,4]
[null,"n = Fixed number of trials = sample size = # of cards pulled = number_sample =",null,null,null,null,null,null,null,null,null,null,2]
[null,"X = Random Discrete Variable that counts successes in sample = # of Queen cards selected in sample = sample_s =",null,null,null,null,null,null,null,null,null,null,2]
[]
[null,"Goal: P(Pull 2 straight Queens from deck of cards without replacement) ="]
[]
[null,null,"This means the sample space will change and the events are not independent."]
[null,null,"We will have to use Conditional Probability and the probability of success is NOT the same for each trial."]
[]
[null,null,"Because there is only one sample point, we can manually calculate it this way:"]
[]
[null,null,"Sample Points =",null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G29:G32),\"\")","v":""}]
[null,null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,null,null,null,null,""]
[null,null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,null,null,null,null,""]
[null,null,"P(Q2 AND Q1) =",null,null,null,null,null,null,null,""]
[]
[]
[]
[null,"Hypergeometric Distribution"]
[null,"Similar to Binomial Distribution except: 1) the trails are not independent AND 2) the probability of success changes from trial to trial."]
[null,"In Excel use: HYPGEOM.DIST(x,n,population_s,number_pop,cumulative)"]
[null,"x = Number of Successes in Sample = Discrete Random Variable = sample_s"]
[null,"n = Trials/Steps in Experiment = Sample Size = number_sample"]
[null,"Number Successes in Pop. =  population_s"]
[null,"Population Size = number_pop"]
[null,"cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x"]
[null,"OR"]
[null,"cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]
[]
[]
[null,"Example 2:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Goal: Calculate the probability that you can pull 2 Face Cards in 5 tries from a deck of cards (without replacement)?"]
[]
[null,"Experiment variables:"]
[null,"Population size = # of cards in deck = number_pop =",null,null,null,null,null,null,null,null,null,null,52]
[null,"Successes in population = # of Queen cards in population = population_s =",null,null,null,null,null,null,null,null,null,null,12]
[null,"n = Fixed number of trials = sample size = # of cards pulled = number_sample =",null,null,null,null,null,null,null,null,null,null,5]
[null,"X = Random Discrete Variable that counts successes in sample = # of Queen cards selected in sample = sample_s =",null,null,null,null,null,null,null,null,null,null,2]
[]
[null,"Goal: P(Pull 2 Face Cards in 5 tries from a deck of cards without replacement) ="]
[]
[null,null,"Sample space will change and the events are not independent."]
[null,null,"Must use Conditional Probability. The probability of success is NOT the same for each trial."]
[]
[null,null,"But this event has many sample points:"]
[]
[null,null,"Sample Points =",null,null,null,{"$f":"COMBIN(M65,M66)","v":10},null,null,null,{"$f":"_xlfn.IFNA(IF(M66=\"\",\"\",_xlfn.FORMULATEXT(G75:G77)),\"\")","v":"=COMBIN(M65,M66)"}]
[null,null,"P(2 Face Cards in 5 Tries) =",null,null,null,null,null,null,null,""]
[null,null,"P(2 Face Cards in 5 Tries) =",null,null,null,null,null,null,null,""]
[]
[null,"Sample Point","Step 1","Step 2","Step 3","Step 4","Step 5","Prob."]
[null,{"$f":"_xlfn.SEQUENCE(G75)","v":1},"F","F","NF","NF","NF",{"$f":"12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48","v":2.5090036014405754E-2},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H80:H89),\"\")","v":"=12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48"}]
[null,2,"F","NF","F","NF","NF",{"$f":"12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48"]
[null,3,"F","NF","NF","F","NF",{"$f":"12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48"]
[null,4,"F","NF","NF","NF","F",{"$f":"12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48"]
[null,5,"NF","F","F","NF","NF",{"$f":"(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48"]
[null,6,"NF","F","NF","F","NF",{"$f":"(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48"]
[null,7,"NF","F","NF","NF","F",{"$f":"(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48"]
[null,8,"NF","NF","F","F","NF",{"$f":"(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48"]
[null,9,"NF","NF","F","NF","F",{"$f":"(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48","v":2.5090036014405761E-2},null,"=(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48"]
[null,10,"NF","NF","NF","F","F",{"$f":"(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48"]
[]
[null,"Example 3:"]
[null,"For the experiment of pulling 5 cards from deck of cards without replacement, and the X Discrete Variable = # of Face Cards pulled, here are the probabilities for all possible X values:"]
[]
[null,"X = # Face Cards","P(X)",null,"Experiment variables:"]
[null,{"$f":"_xlfn.SEQUENCE(M65+1,,0)","v":0},null,null,"Population size = number_pop =",null,null,null,null,52,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(C95),\"\")","v":""}]
[null,1,null,null,"Successes in population = population_s =",null,null,null,null,12]
[null,2,null,null,"n = Fixed number of trials = number_sample =",null,null,null,null,5]
[null,3,null,null,"X = counts successes in sample =  sample_s =",null,null,null,null,2]
[null,4]
[null,5]
[null,"Total",null,null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(C101),\"\")","v":""}]
[]
[null,"Example 4:"]
[null,"Calculate the probability of getting 0 Face cards OR 1 face card OR 2 face cards in 5 tries:"]
[null,"X","P(X)",{"$f":"\"P(x<=\"&B106&\")\"","v":"P(x<=2)"}]
[null,2,{"$f":"\"P(x<=\"&B106&\")\"","v":"P(x<=2)"},null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D106:D107),\"\")","v":""}]
[null,2,{"$f":"\"P(x<=\"&B107&\")\"","v":"P(x<=2)"},null,null,null,""]
[]
[]
[null,"Example 5:"]
[null,"During the financial crisis of 2008, of the ten biggest banks, only three increase lending after they were given TARP funds of about 2 Billion dollars."]
[null,{"$f":"\"If you took at random sample of \"&G121&\" of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, 3?\"","v":"If you took at random sample of 4 of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, 3?"}]
[]
[null,"Experiment = Asking 4 banks out of 10 without replacement, if they increased lending"]
[null,"Success = Bank increase lending"]
[null,"Discrete Variable = X = # of banks that increased lending"]
[]
[null,"Experiment variables:",null,null,null,null,null,null,null,"X","P(X)"]
[null,"Population size = number_pop =",null,null,null,null,10,null,null,{"$f":"_xlfn.SEQUENCE(G121+1,,0)","v":0},null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(K119),\"\")","v":""}]
[null,"Successes in population = population_s =",null,null,null,null,3,null,null,1]
[null,"n = Fixed number of trials = number_sample =",null,null,null,null,4,null,null,2]
[null,"X1 = counts successes in sample =  sample_s =",null,null,null,null,1,null,null,3]
[null,"X2 = counts successes in sample =  sample_s =",null,null,null,null,3,null,null,4]
[null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(_xlfn.ANCHORARRAY(K119))","v":{"$error":"#REF!"}}]
[null,"Goals:"]
[null,null,"Sample Points for 1 in 4 =",null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G126:G130),\"\")","v":""}]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,null,null,""]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7*G126","v":0},null,"=3/10*(9-2)/9*(8-2)/8*(7-2)/7*G126"]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,null,null,""]
[null,null,"P(3 of 4 banks increased lending)",null,null,null,null,null,""]
[]
[null,"Sample Point","Step 1","Step 2","Step 3","Step 4","Prob."]
[null,1,"Lend","Not Lend","Not Lend","Not Lend",{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7","v":0.125},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G133:G136),\"\")","v":"=3/10*(9-2)/9*(8-2)/8*(7-2)/7"}]
[null,2,"Not Lend","Lend","Not Lend","Not Lend",{"$f":"7/10*3/9*(8-2)/8*(7-2)/7","v":0.12499999999999997},null,"=7/10*3/9*(8-2)/8*(7-2)/7"]
[null,3,"Not Lend","Not Lend","Lend","Not Lend",{"$f":"7/10*(7-1)/9*3/8*(7-2)/7","v":0.12499999999999997},null,"=7/10*(7-1)/9*3/8*(7-2)/7"]
[null,4,"Not Lend","Not Lend","Not Lend","Lend",{"$f":"7/10*(7-1)/9*(7-2)/8*3/7","v":0.12499999999999999},null,"=7/10*(7-1)/9*(7-2)/8*3/7"]

{"sheet":"HYPGEOM.DIST (an)","index":45,"n_rows":136,"n_cols":13,"rows_kept":136,"cut":false,"hidden":false,"merged":[[91,1,91,13]]}
[]
[null,"Example 1:"]
[]
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[]
[null,"Goal: Calculate the probability that you can pull 2 straight Queens from a deck of cards (without replacement)?"]
[]
[null,"Experiment variables:"]
[null,"Population size = # of cards in deck = number_pop =",null,null,null,null,null,null,null,null,null,null,52]
[null,"Successes in population = # of Queen cards in population = population_s =",null,null,null,null,null,null,null,null,null,null,4]
[null,"n = Fixed number of trials = sample size = # of cards pulled = number_sample =",null,null,null,null,null,null,null,null,null,null,2]
[null,"X = Random Discrete Variable that counts successes in sample = # of Queen cards selected in sample = sample_s =",null,null,null,null,null,null,null,null,null,null,2]
[]
[null,"Goal: P(Pull 2 straight Queens from deck of cards without replacement) ="]
[]
[null,null,"This means the sample space will change and the events are not independent."]
[null,null,"We will have to use Conditional Probability and the probability of success is NOT the same for each trial."]
[]
[null,null,"Because there is only one sample point, we can manually calculate it this way:"]
[]
[null,null,"Sample Points =",null,null,null,{"$f":"COMBIN(M19,M20)","v":1},null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G29:G32),\"\")","v":"=COMBIN(M19,M20)"}]
[null,null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,{"$f":"4/52*(4-1)/(52-1)","v":4.5248868778280547E-3},null,null,null,"=4/52*(4-1)/(52-1)"]
[null,null,"P(Q2 AND Q1) = P(Q1)* P(Q2 | Q1) =",null,null,null,{"$f":"M18/M17*(M18-1)/(M17-1)","v":4.5248868778280547E-3},null,null,null,"=M18/M17*(M18-1)/(M17-1)"]
[null,null,"P(Q2 AND Q1) =",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(M20,M19,M18,M17,0)","v":4.5248868778280521E-3},null,null,null,"=HYPGEOM.DIST(M20,M19,M18,M17,0)"]
[]
[]
[]
[null,"Hypergeometric Distribution"]
[null,"Similar to Binomial Distribution except: 1) the trails are not independent AND 2) the probability of success changes from trial to trial."]
[null,"In Excel use: HYPGEOM.DIST(x,n,population_s,number_pop,cumulative)"]
[null,"x = Number of Successes in Sample = Discrete Random Variable = sample_s"]
[null,"n = Trials/Steps in Experiment = Sample Size = number_sample"]
[null,"Number Successes in Pop. =  population_s"]
[null,"Population Size = number_pop"]
[null,"cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x"]
[null,"OR"]
[null,"cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]
[]
[]
[null,"Example 2:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Goal: Calculate the probability that you can pull 2 Face Cards in 5 tries from a deck of cards (without replacement)?"]
[]
[null,"Experiment variables:"]
[null,"Population size = # of cards in deck = number_pop =",null,null,null,null,null,null,null,null,null,null,52]
[null,"Successes in population = # of Queen cards in population = population_s =",null,null,null,null,null,null,null,null,null,null,12]
[null,"n = Fixed number of trials = sample size = # of cards pulled = number_sample =",null,null,null,null,null,null,null,null,null,null,5]
[null,"X = Random Discrete Variable that counts successes in sample = # of Queen cards selected in sample = sample_s =",null,null,null,null,null,null,null,null,null,null,2]
[]
[null,"Goal: P(Pull 2 Face Cards in 5 tries from a deck of cards without replacement) ="]
[]
[null,null,"Sample space will change and the events are not independent."]
[null,null,"Must use Conditional Probability. The probability of success is NOT the same for each trial."]
[]
[null,null,"But this event has many sample points:"]
[]
[null,null,"Sample Points =",null,null,null,{"$f":"COMBIN(M65,M66)","v":10},null,null,null,{"$f":"_xlfn.IFNA(IF(M66=\"\",\"\",_xlfn.FORMULATEXT(G75:G77)),\"\")","v":"=COMBIN(M65,M66)"}]
[null,null,"P(2 Face Cards in 5 Tries) =",null,null,null,{"$f":"SUM(H80:H89)","v":0.25090036014405764},null,null,null,"=SUM(H80:H89)"]
[null,null,"P(2 Face Cards in 5 Tries) =",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(M66,M65,M64,M63,0)","v":0.2509003601440577},null,null,null,"=HYPGEOM.DIST(M66,M65,M64,M63,0)"]
[]
[null,"Sample Point","Step 1","Step 2","Step 3","Step 4","Step 5","Prob."]
[null,{"$f":"_xlfn.SEQUENCE(G75)","v":1},"F","F","NF","NF","NF",{"$f":"12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48","v":2.5090036014405754E-2},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(H80:H89),\"\")","v":"=12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48"}]
[null,2,"F","NF","F","NF","NF",{"$f":"12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48"]
[null,3,"F","NF","NF","F","NF",{"$f":"12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48"]
[null,4,"F","NF","NF","NF","F",{"$f":"12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48"]
[null,5,"NF","F","F","NF","NF",{"$f":"(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48"]
[null,6,"NF","F","NF","F","NF",{"$f":"(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48"]
[null,7,"NF","F","NF","NF","F",{"$f":"(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48"]
[null,8,"NF","NF","F","F","NF",{"$f":"(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48"]
[null,9,"NF","NF","F","NF","F",{"$f":"(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48","v":2.5090036014405761E-2},null,"=(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48"]
[null,10,"NF","NF","NF","F","F",{"$f":"(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48"]
[]
[null,"Example 3:"]
[null,"For the experiment of pulling 5 cards from deck of cards without replacement, and the X Discrete Variable = # of Face Cards pulled, here are the probabilities for all possible X values:"]
[]
[null,"X = # Face Cards","P(X)",null,"Experiment variables:"]
[null,{"$f":"_xlfn.SEQUENCE(M65+1,,0)","v":0},{"$f":"_xlfn.HYPGEOM.DIST(_xlfn.ANCHORARRAY(B95),J97,J96,J95,0)","v":0.25318127250900352},null,"Population size = number_pop =",null,null,null,null,52,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(C95),\"\")","v":"=HYPGEOM.DIST(B95#,J97,J96,J95,0)"}]
[null,1,0.42196878751500583,null,"Successes in population = population_s =",null,null,null,null,12]
[null,2,0.2509003601440577,null,"n = Fixed number of trials = number_sample =",null,null,null,null,5]
[null,3,6.6026410564225743E-2,null,"X = counts successes in sample =  sample_s =",null,null,null,null,2]
[null,4,7.6184319881798905E-3]
[null,5,3.047372795271953E-4]
[null,"Total",{"$f":"SUM(_xlfn.ANCHORARRAY(C95))","v":0.99999999999999989},null,null,null,null,null,null,null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(C101),\"\")","v":"=SUM(C95#)"}]
[]
[null,"Example 4:"]
[null,"Calculate the probability of getting 0 Face cards OR 1 face card OR 2 face cards in 5 tries:"]
[null,"X","P(X)",{"$f":"\"P(x<=\"&B106&\")\"","v":"P(x<=2)"}]
[null,2,{"$f":"\"P(x<=\"&B106&\")\"","v":"P(x<=2)"},{"$f":"SUM(C95:C97)","v":0.92605042016806705},null,null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(D106:D107),\"\")","v":"=SUM(C95:C97)"}]
[null,2,{"$f":"\"P(x<=\"&B107&\")\"","v":"P(x<=2)"},{"$f":"_xlfn.HYPGEOM.DIST(B107,J97,J96,J95,1)","v":0.92605042016806716},null,null,"=HYPGEOM.DIST(B107,J97,J96,J95,1)"]
[]
[]
[null,"Example 5:"]
[null,"During the financial crisis of 2008, of the ten biggest banks, only three increase lending after they were given TARP funds of about 2 Billion dollars."]
[null,{"$f":"\"If you took at random sample of \"&G121&\" of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, 3?\"","v":"If you took at random sample of 4 of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, 3?"}]
[]
[null,"Experiment = Asking 4 banks out of 10 without replacement, if they increased lending"]
[null,"Success = Bank increase lending"]
[null,"Discrete Variable = X = # of banks that increased lending"]
[]
[null,"Experiment variables:",null,null,null,null,null,null,null,"X","P(X)"]
[null,"Population size = number_pop =",null,null,null,null,10,null,null,{"$f":"_xlfn.SEQUENCE(G121+1,,0)","v":0},{"$f":"_xlfn.HYPGEOM.DIST(_xlfn.ANCHORARRAY(J119),G121,G120,G119,0)","v":0.1666666666666666},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(K119),\"\")","v":"=HYPGEOM.DIST(J119#,G121,G120,G119,0)"}]
[null,"Successes in population = population_s =",null,null,null,null,3,null,null,1,0.49999999999999994]
[null,"n = Fixed number of trials = number_sample =",null,null,null,null,4,null,null,2,0.30000000000000004]
[null,"X1 = counts successes in sample =  sample_s =",null,null,null,null,1,null,null,3,3.3333333333333291E-2]
[null,"X2 = counts successes in sample =  sample_s =",null,null,null,null,3,null,null,4,0]
[null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(_xlfn.ANCHORARRAY(K119))","v":0.99999999999999989}]
[null,"Goals:"]
[null,null,"Sample Points for 1 in 4 =",null,null,null,{"$f":"COMBIN(G121,G122)","v":4},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G126:G130),\"\")","v":"=COMBIN(G121,G122)"}]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"SUM(G133:G136)","v":0.49999999999999994},null,"=SUM(G133:G136)"]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7*G126","v":0.5},null,"=3/10*(9-2)/9*(8-2)/8*(7-2)/7*G126"]
[null,null,"P(1 of 4 banks increased lending)",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(G122,G121,G120,G119,0)","v":0.49999999999999994},null,"=HYPGEOM.DIST(G122,G121,G120,G119,0)"]
[null,null,"P(3 of 4 banks increased lending)",null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(G123,G121,G120,G119,0)","v":3.3333333333333291E-2},null,"=HYPGEOM.DIST(G123,G121,G120,G119,0)"]
[]
[null,"Sample Point","Step 1","Step 2","Step 3","Step 4","Prob."]
[null,1,"Lend","Not Lend","Not Lend","Not Lend",{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7","v":0.125},null,{"$f":"_xlfn.IFNA(_xlfn.FORMULATEXT(G133:G136),\"\")","v":"=3/10*(9-2)/9*(8-2)/8*(7-2)/7"}]
[null,2,"Not Lend","Lend","Not Lend","Not Lend",{"$f":"7/10*3/9*(8-2)/8*(7-2)/7","v":0.12499999999999997},null,"=7/10*3/9*(8-2)/8*(7-2)/7"]
[null,3,"Not Lend","Not Lend","Lend","Not Lend",{"$f":"7/10*(7-1)/9*3/8*(7-2)/7","v":0.12499999999999997},null,"=7/10*(7-1)/9*3/8*(7-2)/7"]
[null,4,"Not Lend","Not Lend","Not Lend","Lend",{"$f":"7/10*(7-1)/9*(7-2)/8*3/7","v":0.12499999999999999},null,"=7/10*(7-1)/9*(7-2)/8*3/7"]