Question

on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 50. find the z - score of a person who scored 250 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 $x=250$, $\mu=300$, $\sigma=50$ into the formula:
$z = \frac{250 - 300}{50}$

Step3: Calculate numerator and denominator

First compute the numerator: $250 - 300 = -50$. Then divide by the standard deviation:
$z = \frac{-50}{50}$

Step4: Simplify to get z-score

$z = -1$

Answer:

$-1$