Guys... Sorry about missing the 1/8. This is from
KAPLAN CATs. I liked the question. Kudos me if you like the OQ, OA and OE:
Choice (B) is correct; to be within three standard deviations of the mean means to be within 3*(1/8) = 0.375 of the mean. The mean is - 1, so to be within 0.375 of - 1 means to be greater than - 1 - 0.375 = - 1.375 and less than - 1 + 0.375 = - 0.625. The only integer within (three standard deviations) of the mean, i.e., the only integer in the interval - 1.375 to - 0.625, where the endpoints - 1.375 and - 0.625 are not included, is the mean itself, - 1.
Choice (A) is incorrect; it might arise from the thinking that 3/8 isn't big enough to get to another integer, and so the answer would be 0.
Choice (B) is correct, as stated above.
Choice (C) is wrong; it might come from incorrectly associating 3 standard deviations with the number 3 as an answer. Also, the student might incorrectly believe that all Bell Curves have the standard Normal distribution, with a mean of 0 and a standard deviation of 1. Thus, 3 times a standard deviation of 1 might suggest an answer of 3.
Choice (D) is wrong; the student might incorrectly believe that all Bell Curves have the standard Normal distribution. Thus, three standard deviations on each side of the mean, might suggest an answer of 6.
Choice (E) is wrong; this is the number of integers in the interval (including the endpoints) from – 3 to +3. The student might incorrectly believe that all Bell Curves have the standard Normal distribution. Thus, three standard deviations of 1 from the mean 0 might suggest an answer of 7 integers in the interval from - 3 to 3, when the endpoints - 3 and 3 are included.