Question

question
on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. find the z-score of a person who scored 294 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 $x = 294$, $\mu=300$, and $\sigma = 20$.

Step3: Substitute the values into the formula

Substitute $x = 294$, $\mu = 300$, and $\sigma=20$ into the z - score formula:
$z=\frac{294 - 300}{20}$
First, calculate the numerator: $294-300=-6$
Then, divide by the standard deviation: $z=\frac{-6}{20}=-0.3$

Answer:

The z - score is $-0.3$.