Question

on a standardized exam, the scores are normally distributed with a mean of 350 and a standard deviation of 25. find the z - score of a person who scored 415 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 $\mu = 350$, $\sigma=25$, and $x = 415$.

Step3: Substitute values into formula

$z=\frac{415 - 350}{25}=\frac{65}{25}=2.6$

Answer:

$2.6$