In Melanie's Styling Salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standard deviation of 4 minutes. For a simple haircut, the middle 90 percent of the customers will require:
A)between 18.4 and 31.6 minutes.
B)between 19.9 and 30.1 minutes.
C)between 20.0 and 30.0 minutes.
D)between 17.2 and 32.8 minutes.

Question

Quizplus · Accepted Answer

The middle 90% corresponds to the 5th and 95th percentiles of a normal distribution. Using the Z-score formula, Z = (X - μ) / σ, and knowing that the Z-scores for the 5th and 95th percentiles are approximately -1.645 and 1.645, respectively, we can solve for X: X = Zσ + μ. For the 5th percentile, X = -1.645(4) + 25 = 18.42, and for the 95th percentile, X = 1.645(4) + 25 = 31.58. Therefore, the middle 90% of the times are between 18.4 and 31.6 minutes.

In Melanie's Styling Salon, the Time to Complete a Simple