Question

College freshmen took a psychology exam. If the mean is 80, the SD is 10, and the scores have normal distribution, what percent of students failed the test (grade<0)?

2%
34%
14%
48%

Answer 1

(a) 2%

Explanation:

A score of 60 is 2 standard deviations below the mean (80 -2·10 = 60). The empirical rule tells you that 95% of the distribution is within 2 standard deviations of the mean. The remaining 5% is split evenly between those that are more than 2 SD above the mean and those that are more than 2 SD below the mean.

That tells you the percentage who failed is about 2.5%. The best answer choice is 2%.

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Additional comment

The empirical rule is a little bit sloppy, but it gets you in the ballpark. The actual percentage is closer to 2.275%.