Question

on a standardized exam, the scores are normally distributed with a mean of 21 and a standard deviation of 5. find the z-score of a person who scored 11 on the exam.

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We are given that $x = 11$, $\mu=21$, and $\sigma = 5$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{11 - 21}{5}$.

Step4: Simplify the expression

First, calculate the numerator: $11-21=- 10$. Then divide by the standard deviation: $z=\frac{-10}{5}=-2$.

Answer:

-2