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.Complete the following statement: Only 20% of the individuals wait less than _____ minutes.
A)36.72
B)23.28
C)34.63
D)25.37

Question

Quizplus · Accepted Answer

We need to find the value corresponding to the 20th percentile of the normal distribution with mean = 30 and standard deviation = 8. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 20th percentile is -0.84.

Now we can use the formula:

z = (x - μ) / σ

where z is the z-score, μ is the mean, σ is the standard deviation, and x is the value we're trying to find.

Plugging in the values we know, we get:

-0.84 = (x - 30) / 8

Solving for x, we get:

x = 23.28

Therefore, only 20% of the individuals wait less than 23.28 minutes. So, the answer is B.

Suppose That the Waiting Time for a License Plate Renewal