Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes.Suppose that in an effort to provide better service to the public,the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time.The director decides that 15 percent of the customers should receive this discount.What are the numbers of minutes they need to wait to receive the discount?
A)34.48
B)21.68
C)38.32
D)25.52

Question

Quizplus · Accepted Answer

To find the waiting time for customers who receive the discount, we need to find the z-score that marks the 15th percentile of the normal distribution. We can find this value using a standard normal distribution table or calculator.

From the table, we find that the z-score corresponding to the 15th percentile is approximately -1.04.

z = (x - μ) / σ

-1.04 = (x - 30) / 8

x - 30 = -8.32

x = 38.32

Therefore, customers who wait for more than 38.32 minutes will receive the discount. The answer is C) 38.32.

Suppose That the Waiting Time for a License Plate Renewal