The distribution of the scores on a standardized test is

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

The distribution of the scores on a standardized test is

by BTGmoderatorRO » Sun Mar 25, 2018 8:03 am

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%

I do not know the answer to this problem. Please, i want some experts to assist me. Thanks

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Source: Beat The GMAT — Problem Solving | Sun Mar 25, 2018 8:03 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Sun Mar 25, 2018 10:25 pm

Roland2rule 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%

I do not know the answer to this problem. Please, i want some experts to assist me. Thanks

Since the distribution of the scores is bell-shaped and is symmetric about its mean, the percentage of scores greater than (M + S) and the percentage of scores lesser than (M - S) are equal.

The percentage of scores greater than (M + S) plus the percentage of scores lesser than (M - S) = 100 - 68 = 32%.

We have the percentage of scores greater than (M + S) = the percentage of scores lesser than (M - S) = 32/2 = 16%

The correct answer: C

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri May 24, 2019 1:19 pm

BTGmoderatorRO 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.

Answer: C

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