Question

question
on a standardized exam, the scores are normally distributed with a mean of 750 and a standard deviation of 100. find the z-score of a person who scored 675 on the exam.

Explanation:

Step1: Recall the 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 the values

We are given that $x = 675$, $\mu=750$, and $\sigma = 100$.

Step3: Substitute the values into the formula

Substitute the values into the z - score formula: $z=\frac{675 - 750}{100}$.
First, calculate the numerator: $675-750=-75$.
Then, divide by the standard deviation: $z=\frac{-75}{100}=-0.75$.

Answer:

The z - score is $- 0.75$.