Question

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

Answer 1

The answer to the question is

The percent of the distribution is less than m + d is 84 %

Explanation:

To solve the question we list out the variables

Percentage of distribution between m +d and m - d = 68 %

Therefore percentage that are outside the range of m + d and m - d = 32 %

For symmetry to be maintained, of the 32 % that are outside the range of m + d and m - d, 16 % are on either side of the range m + d to m - d

That is 16 % < (m-d) ↔ (m+d)< 16% total range = 100 %

Therefore the proportion of the range lesser than m+d = 100 - 16 or 84 %