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% 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

We need to find the waiting time that corresponds to the 15th percentile, which is the value that separates the lowest 15% of waiting times from the rest.

Using a standard normal distribution table, we can find the z-score that corresponds to the 15th percentile:

z = invNorm(0.15) = -1.036

We can then use the formula:

z = (x - mu) / sigma

where x is the waiting time we're looking for, mu is the mean waiting time, and sigma is the standard deviation.

Plugging in the values we have:

-1.036 = (x - 30) / 8

Solving for x, we get:

x = 38.32

So customers who have to wait for 38.32 minutes or more should receive the discount. Therefore, the best choice is C).

Suppose That the Waiting Time for a License Plate Renewal