Question

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.

Answer 1

The Z-score is calculated by the formula below

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

Step 2: Substitute the given parameters in the formula

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

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