on a standardized exam, the scores are normally distributed with a mean of 165 and a standard deviation of…

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 165$, $\sigma=50$, and $x = 315$.

Step3: Substitute values into formula

$z=\frac{315 - 165}{50}=\frac{150}{50}$

Step4: Calculate the z - score

$\frac{150}{50}=3$

Answer:

3