Standard Deviation

joinn wrote:The class mean score on a test was 60, and the standard deviation was 15. If Elena's
score was within 2 standard deviations of the mean, what is the lowest score she
could have received?

Pals could anyone please explain in detail as I am not satisfied with the manhattan gmat word book's explanation.

Standard deviation measures the dispersion of values +/- around the mean

so if the mean = 60 and standard deviation = 15, then the value that's 1 standard deviation above the mean = 60 + 15 = 75

above the mean by 2 Std = 60 + 2(15) = 90

below the mean by 1 std = 60 - 15 = 45

here they want her lowest score, i.e below the mean, and that score is 2 Stds below the mean

so 60 - 2(15) = 60 -30 = 30

Hi,
If mean is denoted by m and standard deviation by d, then the numbers which are within 'n' standard deviations from mean are the ones in the range [m -n*d, m+n*d]
So, in this case the range of Elena's score is [60-2*15, 60+2*15] i.e. [30, 90]
So, the lowest score is 30.

lowest score will be mean - 2d.

60-2*15 = 30.