Question

on a standardized exam, the scores are normally distributed with a mean of 100 and a standard deviation of 20. find the z - score of a person who scored 130 on the exam.

Explanation:

Step1: Recall z-score formula

The formula for z-score 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 $x=130$, $\mu=100$, $\sigma=20$ into the formula:
$z = \frac{130 - 100}{20}$

Step3: Calculate the result

Simplify the numerator first, then divide:
$z = \frac{30}{20} = 1.5$

Answer:

1.5