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 changing its fee structure so that anyone who uses the phone less than 250 minutes during a given month will pay a reduced monthly fee. Based on the available information, what percentage of current customers would be eligible for the reduced fee?
A) About 36.4 percent
B) Approximately 52 percent
C) About 86.6 percent
D) About 13.6 percent

Question

Quizplus · Accepted Answer

To find the percentage of customers who use less than 250 minutes, we calculate the z-score for 250 minutes using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X = 250$ minutes, $\mu = 445.5$ minutes is the mean, and $\sigma = 177.8$ minutes is the standard deviation. Plugging in the values, we get $z = \frac{(250 - 445.5)}{177.8}$. This calculation results in a z-score that corresponds to the lower tail of the normal distribution. Looking up this z-score in a standard normal distribution table or using a calculator, we find that it corresponds to approximately 13.6 percent of the area under the curve, indicating that about 13.6 percent of customers use less than 250 minutes and would be eligible for the reduced fee.

A Major Cell Phone Service Provider Has Determined That the Number