Question

on a standardized exam, the scores are normally distributed with a mean of 500 and a standard deviation of 40. find the z - score of a person who scored 616 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 $x=616$, $\mu=500$, $\sigma=40$ into the formula:
$z = \frac{616 - 500}{40}$

Step3: Calculate numerator first

$616 - 500 = 116$

Step4: Compute final z-score

$z = \frac{116}{40} = 2.9$

Answer:

2.9