Question

on a standardized exam, the scores are normally distributed with a mean of 135 and a standard deviation of 25. find the z - score of a person who scored 210 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 $x=210$, $\mu=135$, $\sigma=25$ into the formula:
$z = \frac{210 - 135}{25}$

Step3: Calculate numerator first

$210 - 135 = 75$

Step4: Compute final z-score

$z = \frac{75}{25} = 3$

Answer:

3