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.What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes?
A)1.00
B).9699
C).5000
D).9398

Question

Quizplus · Accepted Answer

We can standardize the distribution using the z-score formula:

z = (x - mu)/sigma

where x is the waiting time, mu is the mean, and sigma is the standard deviation.

For x = 15 minutes: 
z = (15 - 30)/8 = -1.875

For x = 45 minutes: 
z = (45 - 30)/8 = 1.875

Using a standard normal distribution table or calculator, we can find the probability that z is between -1.875 and 1.875:

P(-1.875 < z < 1.875) = 0.9398

Therefore, the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes is 0.9398 or 93.98%, which corresponds to choice D.

Suppose That the Waiting Time for a License Plate Renewal