Question

question
on a standardized exam, the scores are normally distributed with a mean of 400 and a standard deviation of 20. find the z - score of a person who scored 460 on the exam.

Explanation:

Step1: Recall the z - score formula

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

Step2: Identify the values

We are given that $x = 460$, $\mu=400$, and $\sigma = 20$.

Step3: Substitute the values into the formula

Substitute $x = 460$, $\mu = 400$, and $\sigma=20$ into the formula $z=\frac{x - \mu}{\sigma}$. We get $z=\frac{460 - 400}{20}$.

Step4: Simplify the expression

First, calculate the numerator: $460-400 = 60$. Then, divide by the denominator: $\frac{60}{20}=3$.

Answer:

The z - score is 3.