Question

select the correct answer from the drop - down menu. the number of books borrowed from a library each week follows a normal distribution. when a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. there is a % chance that more than 250 books were borrowed in a week.

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 250$, $\mu=190$, and $\sigma = 30$.
$z=\frac{250 - 190}{30}=\frac{60}{30}=2$

Step2: Use the properties of the normal distribution

In a normal distribution, about 95% of the data lies within $z=- 2$ and $z = 2$. So the percentage of data outside of this range (either $z>2$ or $z < - 2$) is $100\%-95\% = 5\%$. Since the normal distribution is symmetric, the percentage of data with $z>2$ is $\frac{5\%}{2}=2.5\%$.

Answer:

2.5