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 315 on the exam.

Answer 1

3

Step-by-step explanation:

`z=(x-μ)/(σ)`

`z=(360-300)/(20)`

`z=(60)/(20)`

`z=3`

They scored 3 standard deviations above the mean

(Which is better than 99.9% of test takers)

Answer 2

Answer: 0.75

Step-by-step explanation:

Mean(μ) = 300

Standard deviation(σ) = 20

Find the z-score of a person who scored 315 on the exam ;

Raw score (x) = 315

Z = (raw score - mean) ÷ standard deviation

Z = (x - μ) ÷ σ

Z = (315 - 300) ÷ 20

Z = 15 ÷ 20

Z = 0.75