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A certain characteristic in a large population has a

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A certain characteristic in a large population has a [#permalink] New post 12 Dec 2012, 03:19
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49% (02:03) correct 50% (01:14) wrong based on 136 sessions
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 ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
[Reveal] Spoiler: OA
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Re: A certain characteristic in a large population has a [#permalink] New post 12 Dec 2012, 03:26
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Walkabout 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 less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%


Given that 68% lies between m-d and m+d, thus 32% lies out of this range.

Now, since the distribution is symmetric about m, then half of the 32%, so 16%, lies to the right of m+d. Therefore, 16% lies to the right of m+d, and hence 84% lies to the left of m+d, which means that 84% is less than m+d.

Answer: D.

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Re: A certain characteristic in a large population has a [#permalink] New post 20 Oct 2013, 18:29
Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
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Re: A certain characteristic in a large population has a [#permalink] New post 20 Oct 2013, 22:27
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Re: A certain characteristic in a large population has a [#permalink] New post 13 Jan 2014, 01:28
Walkabout 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 less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%



This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.

So, if 68% is one st.Dev, then on either side of m we have 68/2 = 34%. So, 34% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 34 = 84% going from the mean m, to the right of the distribution in the bell shaped histogram.. This means that 84% of the values are below m + d.

Like I said, doing it on a bell-curve histogram is much easier to fully "get" how this works, or you could apply GMAT percentile jargon/theory to it :-D
Re: A certain characteristic in a large population has a   [#permalink] 13 Jan 2014, 01:28
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