select the correct answer. the numbers of pages in the books in a library follow a normal distribution. if…

Answer:

B. About 16% of the books have fewer than 150 pages.

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 150$, $\mu=180$, and $\sigma = 30$. So $z=\frac{150 - 180}{30}=\frac{- 30}{30}=-1$.

Step2: Use the empirical rule

For a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), which means 34% of the data lies between $\mu$ and $\mu - \sigma$. The total percentage of data less than $\mu$ is 50%. So the percentage of data less than $\mu-\sigma$ is $50%-34% = 16%$. Since $x = 150=\mu - \sigma$ (because $\mu=180$ and $\sigma = 30$), about 16% of the books have fewer than 150 pages.