Question

on a standardized exam, the scores are normally distributed with a mean of 185 and a standard deviation of 10. find the z - score of a person who scored 170 on the exam.

Explanation:

Step1: Recall z - score formula

The z - score formula 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 have $x = 170$, $\mu=185$, and $\sigma = 10$.

Step3: Substitute values into formula

$z=\frac{170 - 185}{10}=\frac{- 15}{10}=-1.5$

Answer:

$-1.5$