Question

question
on a standardized exam, the scores are normally distributed with a mean of 700 and a standard deviation of 20. find the z-score of a person who scored 705 on the exam.
answer attempt 1 out of 2

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 $x = 705$, $\mu=700$, and $\sigma = 20$.

Step3: Substitute values into formula

Substitute $x = 705$, $\mu = 700$, and $\sigma=20$ into the formula $z=\frac{x - \mu}{\sigma}$. So we have $z=\frac{705 - 700}{20}$.

Step4: Simplify the expression

First, calculate the numerator: $705-700 = 5$. Then divide by the denominator: $z=\frac{5}{20}=0.25$.

Answer:

0.25