Question

Consider the following Binomial Distribution scenario:

The number of accounts that are in compliance or not in compliance with an accounting procedure

1. Create a hypothetical data set for the above scenario

2. Explain how it is used at the company

Answer 1

1.

Let the probability of accounts in compliance be 0.7. Let the number of accounts in the company be 100. So, this will be the case of a binomial distribution which consists of n=20 trials and results in x successes (accounts that are in complinace equals to x). If the probability of success (accounts in compliance) on an individual trial is P = 0.7, then the binomial probability is:

b(x; n, P) = nCx * P^x * (1 - P)^n-x

A hypothetical data set for the above scenario is

75, 66, 70, 73, 64, 74, 72, 74, 77, 74, 71, 79, 70, 71, 77, 69, 65, 69, 71, 67

It gives the number of accounts that are in compliance out of 100 accounts on different 20 trials.

2.

The company can use it to determine the probability of x accounts in compliance out of n accounts and is given as,

b(x; n, P) = nCx * P^x * (1 - P)^n-x

where P is the probability of an account in complaince.

Also, the company can estimate the mean and variance of the number of accounts in compliance.

Mean number of accounts in compliance = nP

Variance of number of accounts in compliance = nP(1-P)