Question

question
on a standardized exam, the scores are normally distributed with a mean of 40 and a standard deviation of 5. find the z - score of a person who scored 27 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 $x=27$, $\mu=40$, $\sigma=5$ into the formula:
$z = \frac{27 - 40}{5}$

Step3: Calculate numerator first

Compute $27 - 40 = -13$

Step4: Compute final z-score

$z = \frac{-13}{5} = -2.6$

Answer:

$-2.6$