Question

on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. find the z - score of a person who scored 270 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 are given that $\mu = 300$, $\sigma=20$, and $x = 270$.

Step3: Substitute values into formula

$z=\frac{270 - 300}{20}=\frac{- 30}{20}=-1.5$

Answer:

$-1.5$