The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent).The historical records of the company show that over the past 8 years,the average has been that 13 percent of the accounts have been delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What is the probability that no more than 40 accounts will be classified as delinquent?
A)42.07%
B)92.07%
C)7.93%
D)40.15%
E)90.15%

Question

Quizplus · Accepted Answer

The probability that no more than 40 accounts are delinquent can be calculated using the normal approximation to the binomial distribution. With a sample size of 250 and a historical delinquency rate of 13%, the expected number of delinquent accounts is 32.5. The standard deviation is approximately 5.4. Using the normal approximation, the probability of having 40 or fewer delinquent accounts is approximately 92.07%.

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