Question

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that at least 50 accounts will be classified as delinquent? Round your answer to four decimal places.

Answer 1

p = 0.14

n = 250

= n * p = 250 * 0.14 = 35

= sqrt(np(1 - p))

    = sqrt(250 * 0.14 * (1 - 0.14))

    = 5.486

P(X > 50)

= P(X > 49.5)

= P((X - )/> (49.5 - )/)

= P(Z > (49.5 - 35)/5.486)

= P(Z > 2.64)

= 1 - P(Z < 2.64)

= 1 - 0.9959

= 0.0041