arjtryarjtry wrote:

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 more than m-d?

A. 16%

B. 32%

C. 48%

D. 84%

E. 92%

I agree with the D answers.

The question asks what percent of the distribution is

more than m-d. If you picture it like a typical bell curve, m-d is on the left and the question asks for everything to the right of that point.

The population within one standard deviation is 68% (both to the right and the left of the center of the bell curve.) That means half of 68% accounts for the distance from m-d to m: 34%. Then you need everything else that's greater than m, which is half of the entire distribution, or 50%. 50+34 = 84%.

[Not meaning to confuse, but in my head I actually something similar to icandy's way:

( % of distro between m-d and m+d ) + ( % of distro between m+d and 100)

which is same as

( % of distro between m-d and m+d ) + ( half of the % of distro outside of m+d and m-d)

which is (68%) + ((100-68)/2)% = 84%]