Question

on a standardized exam, the scores are normally distributed with a mean of 150 and a standard deviation of 10. find the z - score of a person who scored 127 on the exam.

Explanation:

Step1: Recall z-score formula

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

Step2: Substitute given values

Substitute $x=127$, $\mu=150$, $\sigma=10$ into the formula:
$z = \frac{127 - 150}{10}$

Step3: Calculate the result

First compute the numerator: $127 - 150 = -23$. Then divide by 10:
$z = \frac{-23}{10} = -2.3$

Answer:

$-2.3$