Question

question
on a standardized exam, the scores are normally distributed with a mean of 51 and a standard deviation of 10. find the z - score of a person who scored 27 on the exam.
answer attempt 1 out of 2

Explanation:

Step1: Recall the z - score formula

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

Step2: Identify the values

We are given that $x = 27$, $\mu=51$, and $\sigma = 10$.

Step3: Substitute the values into the formula

Substitute $x = 27$, $\mu = 51$, and $\sigma=10$ into the formula $z=\frac{x - \mu}{\sigma}$. We get $z=\frac{27-51}{10}$.

Step4: Simplify the numerator

First, calculate the numerator: $27-51=- 24$.

Step5: Calculate the z - score

Then, divide the numerator by the denominator: $z=\frac{-24}{10}=-2.4$.

Answer:

-2.4