The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses between 400 and 500 minutes?
A)0.4773
B)0.05228
C)0.0228
D)0.9773

Question

Quizplus · Accepted Answer

To find the probability that a student uses between 400 and 500 minutes, we calculate the z-scores for 400 and 500 minutes and then find the area under the normal distribution curve between these z-scores. The z-score formula is $z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 400 minutes, $z = \frac{400 - 500}{50} = -2$, and for 500 minutes, $z = \frac{500 - 500}{50} = 0$. Looking up these z-scores in a standard normal distribution table or using a calculator, the area between $z = -2$ and $z = 0$ is approximately 0.4773, which corresponds to the probability of a student using between 400 and 500 minutes.

The Number of Cell Phone Minutes Used by High School