Problem Solving - 31

A certain characteristic in a large population has a distribution that is symmetric about the mean m.If 68 percent of the distribution lies within one Standard Deviation d of the mean, what percent of the distribution is less than m+d?
A. 16%
B. 32%
C. 48%
D. 84%
E. 92%

Answer: D
In a normal bell curved distribution, 50% are below the mean and 50% are over it
If 68% are distributed within 1 S.D of the mean then this implies that 34% are 1 S.D above the mean and 34% are 1 S.D below the mean i.e 34% between m and m+d and 34% between m-d and m
The distribution is symmetric about m also => 32/2 = 16% between 0 and m-d and 16% m+d and above.
Hence total that is less than m+d = 100-16 = 84%

OR

Distribution is symmetric around mean => 68/2 = 34% =>(Mean-S.D, Mean) = (Mean, Mean+S.D] = 34% . Thus below Mean+S.D = 50+34 = 84%

NOTE: For a normal bell-curve distribution, the percentage is approx 34% between the mean and 1 S.D. the percentage is approximately 13.6% between 1 SD and 2 SD, the percentage is approximately 2% between 2 S.D and on...