Question

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 350 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 of the dataset, and $\sigma$ is the standard deviation of the dataset.

Step2: Identify values

We are given that $x = 350$, $\mu=300$, and $\sigma = 40$.

Step3: Substitute values into formula

Substitute $x = 350$, $\mu = 300$, and $\sigma=40$ into the z - score formula:
$z=\frac{350 - 300}{40}$
First, calculate the numerator: $350-300 = 50$.
Then, divide by the standard deviation: $z=\frac{50}{40}=1.25$.

Answer:

The z - score is $1.25$.