A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of charging a lower rate for customers who use the phone less than a specified amount. If it wishes to give the rate reduction to no more than 12 percent of its customers, what should the cut-off be?
A) About 237 minutes
B) About 654 minutes
C) About 390 minutes
D) About 325 minutes

Question

Quizplus · Accepted Answer

To find the cut-off for the lower 12% of customers, we need to find the z-score that corresponds to the 12th percentile of a standard normal distribution, which is approximately -1.175. Using the formula X = μ + Zσ, where μ is the mean (445.5), Z is the z-score (-1.175), and σ is the standard deviation (177.8), we calculate the cut-off: X = 445.5 + (-1.175)(177.8) ≈ 237 minutes.

A Major Cell Phone Service Provider Has Determined That the Number