Question

on a standardized exam, the scores are normally distributed with a mean of 250 and a standard deviation of 40. find the z-score of a person who scored 362 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 $x = 362$, $\mu=250$, and $\sigma = 40$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{362 - 250}{40}$.
First, calculate the numerator: $362-250 = 112$.
Then, divide by the standard deviation: $z=\frac{112}{40}=2.8$.

Answer:

The z - score is $2.8$.