Problem 74E

Refer to Exercise 3.73. What are the mean and standard deviation of the number of accounts that must be examined to find the first one with substantial errors?

Reference

A certified public accountant (CPA) has found that nine of ten company audits contain substantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors

a is the third one to be audited?

b will occur on or after the third audited account?

Solution 74E

Step1 of 2:

Let us consider random variable ‘X’ it presents the company audits contain substantial errors.

Here X follows geometric distribution with parameter ‘p’.

That is XGeometric(p)

XGeometric()

Then the probability mass function of geometric distribution is given by:

Where,

x = random variable

p = probability of success(Parameter)

n = sample size

We need to find mean and standard deviation of X.

Step2 of 2:

Mean of the geometric distribution is given by:

= 1.1111

Hence, mean of X is 1.1111.

Now,

Variance of geometric distribution is given by:

Hence, the variance of X is 0.1234.

Standard deviation of X is given by:

= 0.3513

Hence, the Standard deviation of X is 0.3513.