Question

on a standardized exam, the scores are normally distributed with a mean of 29 and a standard deviation of 5. find the z - score of a person who scored 14 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 $x = 14$, $\mu=29$, and $\sigma = 5$.

Step3: Substitute values into formula

$z=\frac{14 - 29}{5}=\frac{-15}{5}$

Step4: Calculate z - score

$z=-3$

Answer:

$-3$