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?
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?
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)
Then the probability mass function of geometric distribution is given by:
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:
Hence, mean of X is 1.1111.
Variance of geometric distribution is given by:
Hence, the variance of X is 0.1234.
Standard deviation of X is given by:
Hence, the Standard deviation of X is 0.3513.