Question

on a standardized exam, the scores are normally distributed with a mean of 500 and a standard deviation of 25. find the z-score of a person who scored 525 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 value from the dataset, $\mu$ is the mean of the dataset, and $\sigma$ is the standard deviation of the dataset.

Step2: Identify the values of $x$, $\mu$, and $\sigma$

We are given that $x = 525$, $\mu=500$, and $\sigma = 25$.

Step3: Substitute the values into the formula

Substitute $x = 525$, $\mu = 500$, and $\sigma=25$ into the formula $z=\frac{x-\mu}{\sigma}$. We get $z=\frac{525 - 500}{25}$.

Step4: Simplify the expression

First, calculate the numerator: $525-500 = 25$. Then, divide by the denominator: $\frac{25}{25}=1$.

Answer:

The z - score is 1.