Question

On a standardized test, the mean is 37 and the standard deviation is 2.5. Approximately what percent of the scores fall in the range 32 - 42 ?

A) 68%
B) 95%
C) 34%
D) 99%

Answer 1

B) 95%

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 37, standard deviation = 2.5

Approximately what percent of the scores fall in the range 32 - 42 ?

32 = 37 - 2*2.5

So 2 standard deviations below the mean

42 = 37 + 2*2.5

So 2 standard deviations above the mean.

This question is the percentage of scores within 2 standard deviations of the mean, so, by the Empirical Rule, it is 95%, option B.