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# A certain characteristic in a large population has a

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Senior Manager
Joined: 05 Jun 2008
Posts: 304

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

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18 Sep 2008, 06:16
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25% (medium)

Question Stats:

61% (00:36) correct 39% (00:25) wrong based on 107 sessions

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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%

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-characteristic-in-a-large-population-has-a-143982.html
[Reveal] Spoiler: OA

Kudos [?]: 199 [0], given: 0

Director
Joined: 12 Jul 2008
Posts: 514

Kudos [?]: 165 [2], given: 0

Schools: Wharton

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18 Sep 2008, 06:30
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vivektripathi 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%

D

The prompt says that 68% of the population lies between m-d and m+d.

Thus, 32% of the population is less than m-d or greater than m+d.

Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.

Thus, (68+16)% or (100-16)% of the population is less than m+d.

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Joined: 07 Nov 2007
Posts: 1791

Kudos [?]: 1088 [2], given: 5

Location: New York

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18 Sep 2008, 06:37
2
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vivektripathi 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%

100-16=84%

D
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Kudos [?]: 1088 [2], given: 5

Intern
Joined: 11 Feb 2013
Posts: 17

Kudos [?]: 6 [1], given: 4

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08 Jun 2013, 10:01
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zoinnk wrote:
vivektripathi 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%

D

The prompt says that 68% of the population lies between m-d and m+d.

Thus, 32% of the population is less than m-d or greater than m+d.

Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.

Thus, (68+16)% or (100-16)% of the population is less than m+d.

Hi Team,

i think i cannot understand the language of these type of questions.
i have the problem of understanding the question language only in standard deviation and mean questions.

if anyone has like 5-10 ques for practice of this sort of questions then please post here for me. Thanks in advance!

Query : in this particular question how does the line " If 68 percent of the distribution lies within one standard deviation d of the mean" means that "The prompt says that 68% of the population lies between m-d and m+d."

Thanks a lot.

Kudos [?]: 6 [1], given: 4

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132517 [3], given: 12324

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08 Jun 2013, 11:10
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Perhaps wrote:
zoinnk wrote:
vivektripathi 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%

D

The prompt says that 68% of the population lies between m-d and m+d.

Thus, 32% of the population is less than m-d or greater than m+d.

Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.

Thus, (68+16)% or (100-16)% of the population is less than m+d.

Hi Team,

i think i cannot understand the language of these type of questions.
i have the problem of understanding the question language only in standard deviation and mean questions.

if anyone has like 5-10 ques for practice of this sort of questions then please post here for me. Thanks in advance!

Query : in this particular question how does the line " If 68 percent of the distribution lies within one standard deviation d of the mean" means that "The prompt says that 68% of the population lies between m-d and m+d."

Thanks a lot.

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.

Similar questions to practice:
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the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html
for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html
given-that-the-mean-of-set-a-is-10-what-is-the-range-of-two-141964.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-characteristic-in-a-large-population-has-a-143982.html In case of any further questions please post in this thread.
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Kudos [?]: 132517 [3], given: 12324

Re: PS-Stat   [#permalink] 08 Jun 2013, 11:10
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