Question

on a standardized exam, the scores are normally distributed with a mean of 135 and a standard deviation of 25. find the z - score of a person who scored 210 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 $x = 210$, $\mu=135$ and $\sigma = 25$.

Step3: Substitute values into formula

$z=\frac{210 - 135}{25}=\frac{75}{25}$

Step4: Calculate z - score

$z = 3$

Answer:

3