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# A certain characteristic in a large population has a

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Senior Manager
Joined: 25 Jun 2009
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Kudos [?]: 120 [1] , given: 6

A certain characteristic in a large population has a [#permalink]

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08 May 2010, 10:57
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56% (01:44) correct 44% (00:51) wrong based on 172 sessions

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A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies 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%

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-characteristic-in-a-large-population-has-a-143982.html
[Reveal] Spoiler: OA
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Joined: 26 Sep 2012
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Kudos [?]: 15 [7] , given: 1

Re: A certain characteristic in a large population has a [#permalink]

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19 Jul 2013, 01:46
7
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The right answer has been given earlier.

In a case like this, to outline the picture is the best way to understand the question stem. Please find the picture below.
I hope it helps.

Sorry for poor painting skills
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Kudos [?]: 93234 [7] , given: 10553

Re: A certain characteristic in a large population has a [#permalink]

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19 Jul 2013, 01:57
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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.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-characteristic-in-a-large-population-has-a-143982.html
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08 May 2010, 11:01
1
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nitishmahajan wrote:
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies 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%

IMO D, whats the OA

16%
________________________________________________ m+d
34%
________________________________________________ m
34%
________________________________________________ m-d

16%

since 68% lies one standard deviation from mean m, => 50% of 68% lies on either side as it is symmetric about m.
thus 16% lie below m-d and 16% lie above m+d

now below m+d = 16+34+34 = 84%
hence D
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Re: Standard Deviation Question..!   [#permalink] 08 May 2010, 11:01
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