Question

the number of music cds sold weekly by a store follows a normal distribution with a mean of 455 and a standard deviation of 65.
which sentence summarizes this information? select the correct answer.
a. there is an 84% chance that the shop sells more than 390 cds in a week.
b. there is an 34% chance that the shop sells more than 390 cds in a week.
c. there is an 84% chance that the shop sells fewer than 390 cds in a week.
d. there is an 68% chance that the shop sells fewer than 390 cds in a week.
e. there is an 95% chance that the shop sells more than 390 cds in a week.

Explanation:

Step1: Calculate the z-score

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x=390$, $\mu=455$, $\sigma=65$.
$z = \frac{390 - 455}{65} = \frac{-65}{65} = -1$

Step2: Use empirical rule for normal distribution

For a normal distribution, about 16% of data lies below $z=-1$. This means $100\% - 16\% = 84\%$ of data lies above $z=-1$.

Answer:

A. There is an 84% chance that the shop sells more than 390 CDs in a week.