Question

on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. find the z-score of a person who scored 400 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 value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $x = 400$, $\mu=300$, and $\sigma = 40$.

Step3: Substitute values into formula

Substitute $x = 400$, $\mu = 300$, and $\sigma=40$ into the formula: $z=\frac{400 - 300}{40}$.

Step4: Calculate numerator and then the fraction

First, calculate the numerator: $400-300 = 100$. Then, divide by the standard deviation: $\frac{100}{40}=2.5$.

Answer:

2.5