n the normal distribution, approximately what percentage of test scores will fall between 2 and 3 standard deviations above the mean?a.2.1%b.34.1%c.13.6%d.68%
Question
In the normal distribution, approximately what percentage of test scores will fall between 2 and 3 standard deviations above the mean?
a. 2.1%
b. 34.1%
c. 13.6%
d. 68%
Solution
The answer is a. 2.1%. In a normal distribution, about 68% of scores fall within one standard deviation of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three standard deviations. Therefore, the percentage of scores that fall between two and three standard deviations above the mean is about 99.7% - 95% = 4.7%. However, since this range is above the mean, we only take half of this percentage, which is about 2.35%. So, approximately 2.1% of scores will fall between 2 and 3 standard deviations above the mean.
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