Assume that a procedure yields a binomial distribution with a trial repeated

Albarellak

Albarellak

Answered question

2021-10-08

Assume that a procedure yields a binomial distribution with a trial repeated n=5 times. Use some form of technology to find the cumulative probability distribution given the probability p=0.774 of success on a single trial.
(Report answers accurate to 4 decimal places.)
kP(X<k)012345

Answer & Explanation

Aubree Mcintyre

Aubree Mcintyre

Skilled2021-10-09Added 73 answers

Step 1
Use PH-stat to obtain the cumulative probability distribution for the given probability.
Let X denotes the random variable which follows binimial distribution with the probability of succes 0.774 with number of trails selected is 5. That is, XB(n=5,p=0.774)
The probability distribution is given by,
P(X=x)=(nx)px(1p)nx here x=0,1,2,,n for 0p1
Where n is the number of trials and p is the probability of success for each trial.
Excel add-in (PHStat)procedure:
1) In EXCEL, Select AddIns>PHStat>Probability & Prob. Distributions
2) Choose Binomial.
3) In Data enter Sample Size as 5 and Prob. of an Event on Interest as 0.774.
4) In Outcomes From and To, enter 0 and 5, respectively.
5) Select Cumulative Probabilities.
6) Click Ok.
Excel add-in (PHStat) output:
DataSample size5Probability of an event of interest0.774
StatisticsMean3.87Variance0.8746Standard deviation0.9352
XP(X)P(X)P(<X)P(>X)P(X)00.00060.00060.00000.99941.000010.01010.01070.00060.98930.999420.06920.07980.01070.92020.989330.23680.31670.07980.68330.920240.40550.72220.31670.27780.683350.27781.00000.72220.00000.2778
Step 2
From the EXCEL output, the cumulative probabilities are as follows:
KP(X<k)00.000010.000620.010730.079840.316750.7222

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