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.

Answer: C

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