Question

this is the only question in this section.
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 285 on the exam.

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the individual score, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

Step2: Identify given values

$x = 285$, $\mu = 300$, $\sigma = 20$

Step3: Substitute values into formula

$z = \frac{285 - 300}{20}$

Step4: Calculate numerator and denominator

$z = \frac{-15}{20} = -0.75$

Answer:

$-0.75$