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The distribution of the scores on a standardized test is bell-shaped a

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Math Expert
Joined: 02 Sep 2009
Posts: 58347
The distribution of the scores on a standardized test is bell-shaped a  [#permalink]

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21 Mar 2018, 23:04
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Difficulty:

15% (low)

Question Stats:

92% (00:58) correct 8% (00:13) wrong based on 38 sessions

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The distribution of the scores on a standardized test is bell-shaped and is symmetric about its mean, M, with a standard deviation, S. If 68% of the scores fall between M - S and M + S, what percent of the scores are greater than M + S?

(A) 4%
(B) 8%
(C) 16%
(D) 32%
(E) 34%

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Joined: 14 Mar 2018
Posts: 10
Re: The distribution of the scores on a standardized test is bell-shaped a  [#permalink]

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21 Mar 2018, 23:07
Bunuel wrote:
The distribution of the scores on a standardized test is bell-shaped and is symmetric about its mean, M, with a standard deviation, S. If 68% of the scores fall between M - S and M + S, what percent of the scores are greater than M + S?

(A) 4%
(B) 8%
(C) 16%
(D) 32%
(E) 34%

32% scores to be distributed equally between <M-S and >M+S
Hence 16%
C
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: The distribution of the scores on a standardized test is bell-shaped a  [#permalink]

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23 Mar 2018, 12:46
Bunuel wrote:
The distribution of the scores on a standardized test is bell-shaped and is symmetric about its mean, M, with a standard deviation, S. If 68% of the scores fall between M - S and M + S, what percent of the scores are greater than M + S?

(A) 4%
(B) 8%
(C) 16%
(D) 32%
(E) 34%

Since 68% of the scores fall between M - S and M + S, then 32% of the scores fall in the two tails of the bell curve. Since the distribution is symmetric about its mean, that means exactly half of 32%, i.e., 16%, of scores fall above M + S (and the other 16% fall below M - S).

Alternate Solution:

Since the distribution is symmetric about its mean, exactly half of 68%, i.e. 34% of the scores fall between M and M + S (and the other 34% fall between M and M - S). Again since the distribution is symmetric about its mean, 50% of the scores fall above M. Then, 50 - 34 = 16% of the scores fall above M + S.

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Re: The distribution of the scores on a standardized test is bell-shaped a   [#permalink] 23 Mar 2018, 12:46
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