Symmetric Distribution

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A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 95 percent of the distribution lies within twice the standard deviation of the mean, where the standard deviation is d, what percent of the distribution is greater than ?

Review: Symmetric Distribution


Explanation

This question describes something that sounds like a normal distribution, although there is no mention of normal distributions in the official test rubric and so we won't have to bust out special statistics knowledge here. The distribution might look something like this:



It's symmetric about the mean m. We're told 95 percent of the distribution lies between and . That means that 5 percent of the distribution lies in the little portion to the left of and the little portion to the right of . Since the distribution is symmetric, regardless of its exact shape, we know those two little portions are equal in size. Therefore the size of one of them must be half of 5 percent, or 2.5%.

The correct answer is (B).


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