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 270 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 $x=270$, $\mu=300$, $\sigma=20$ into the formula:
$z = \frac{270 - 300}{20}$

Step3: Calculate the result

First compute the numerator: $270 - 300 = -30$. Then divide by 20: $z = \frac{-30}{20} = -1.5$

Answer:

$-1.5$