The distribution of the scores on a standardized test is

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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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