On a standardized exam, the scores are normally distributed with a mean of 165 and astandard deviation of 40. Find the z-score of a person who scored 145 on the exam.

Question

asked May 1, 2023 162k views

1 Answer

Gandreadis · Answer 1 · 2023-05-04T16:43:09+0000

The Z-score is calculated by the formula below

$\begin{gathered} z-score=((x-\mu))/(\sigma)_{} \\ \mu=\operatorname{mean} \\ \sigma=s\tan dard\text{ deviation} \\ x=\text{score} \end{gathered}$

Step 2: Substitute the given parameters in the formula

$\begin{gathered} z-\text{score}=(145-165)/(40) \\ Z=-(20)/(40) \\ Z=-(1)/(2) \\ Z=-0.5 \end{gathered}$

Hence, the z-score of a person who scored 145 on the exam is -0.5