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A certain characteristic in a large population has a [#permalink]
05 Sep 2008, 19:03

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%

Re: normal distribution [#permalink]
05 Sep 2008, 19:24

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%

since out of 100 ,68 lie within m-d deviation,32 must lie outside or on the mean !!! A Vs B is answer C,D,E get eliminated since we need values less than or equal to 32 .

since distribution is symmetric about mean m.16% will be the answer IMO A

Re: normal distribution [#permalink]
06 Sep 2008, 04:12

spriya wrote:

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%

since out of 100 ,68 lie within m-d deviation,32 must lie outside or on the mean !!! A Vs B is answer C,D,E get eliminated since we need values less than or equal to 32 .

since distribution is symmetric about mean m.16% will be the answer IMO A

IMO D is the answer.

spriya i think D cannot be eliminated by default.

_________________

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Re: normal distribution [#permalink]
08 Sep 2008, 00:57

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%]

gmatclubot

Re: normal distribution
[#permalink]
08 Sep 2008, 00:57