Question

on a standardized exam, the scores are normally distributed with a mean of 75 and a standard deviation of 10. find the z - score of a person who scored 45 on the exam.

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We are given that $\mu = 75$, $\sigma=10$, and $x = 45$.

Step3: Substitute values into formula

$z=\frac{45 - 75}{10}$.

Step4: Calculate the numerator

$45-75=-30$.

Step5: Calculate the z - score

$z=\frac{-30}{10}=-3$.

Answer:

$-3$