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.
a) What are the mean and the standard deviation of the sampling distribution of ?
b) What is the probability that at least 30 accounts will be classified as delinquent?