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. As a promotion, the company plans to hold a drawing to give away one free vacation to Hawaii for a customer who uses between 400 and 402 minutes during a particular month. Based on the information provided, what proportion of the company's customers would be eligible for the drawing?
A) Approximately 0.1026
B) About 0.004
C) Approximately 0.2013
D) About 0.02

Question

Quizplus · Accepted Answer

To find the proportion of customers who use between 400 and 402 minutes, we need to calculate the z-scores for 400 and 402 minutes and then find the area between these z-scores in a standard normal distribution. The z-score is calculated as $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 400 minutes, $z = \frac{(400 - 445.5)}{177.8}$, and for 402 minutes, $z = \frac{(402 - 445.5)}{177.8}$. Looking these z-scores up in a standard normal distribution table or using a calculator will give us the proportion of the area between these two values, which is approximately 0.004. This represents the proportion of customers using between 400 and 402 minutes.

A Major Cell Phone Service Provider Has Determined That the Number