Problem Solving

95% of the distribution is within two standard deviations of the mean, so 95% of the distribution lies between A - 2SD and A + 2SD. So all of those values are less than A+2SD. The other 5% of the distribution is more than two standard deviations from the mean. Since the distribution is symmetric, half of those values, or 2.5% of the entire distribution, will be less than A-2SD, and the rest will be greater than A+2SD.

So 95% are between A-2SD and A+2SD, and 2.5% are below A-2SD, for a total of 97.5% that are less than A+2SD.

BTGmoderatorDC wrote:The age of a group of people follows a distribution, which is symmetric about the average (mean) A. If 95% of the distribution falls within two standard deviation (SD) of the mean, then what percentage of the same distribution is less than A + 2SD?

A. 68%
B. 84%
C. 95%
D. 97.5%
E. 99%

OA D

Source: e-GMAT

If 95% of the distribution falls within two standard deviation (SD) of the mean, then 2.5% of the distribution falls more than 2 SDs below the mean (and another 2.5% falls more than 2 SDs above the mean). The percentage of the distribution that is less than A + 2SD is the percentage that falls within 2 SDs of the mean plus the percentage that falls more than 2 SDs below the mean. Therefore, the percentage is 95% + 2.5% = 97.5%.

Answer: D