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 $\sigma = 30$. So $z=\frac{250 - 190}{30}=\frac{60}{30}=2$.

Step2: Use the properties of the normal distribution

The total area under the normal - distribution curve is 1. The area to the left of $z = 2$ can be found from the standard normal distribution table, which is approximately 0.9772. The area to the right of $z = 2$ (the probability that $x>250$) is $P(X>250)=1 - P(X\leq250)=1 - 0.9772 = 0.0228\approx2.5\%$.

Answer:

2.5