Question

PLEASE HELP!

On a standardized exam, the scores are normally distributed with a mean of 155 and a standard deviation of 20. Find the z-score of a person who scored 145 on the exam.

Answer 1

Explanation:

z=\frac{x-\mu}{\sigma}

z=

σ

x−μ

​

z-score formula

z=\frac{155-190}{20}

z=

20

155−190

​

Plug in values

z=\frac{-35}{20}

z=

20

−35

​

Subtract

z=-1.75

z=−1.75

Divide

\text{They scored 1.75 standard deviations below the mean.}

They scored 1.75 standard deviations below the mean.

Answer 2

-0.5

Explanation:

z-score = (x- mean)/SD

(145-155)/20 = -10/20 = -0.5