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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.

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Answer: 0.75

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

Answer:

3

Explanation:

[tex]z=\frac{x-μ}{σ}[/tex]

[tex]z=\frac{360-300}{20}[/tex]

[tex]z=\frac{60}{20}[/tex]

[tex]z=3[/tex]

They scored 3 standard deviations above the mean

(Which is better than 99.9% of test takers)

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