Question

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 1

The correct option is D $84\%$

Let Total percentage of population $=100$%

Distribution of population that is $symmetric$ about the mean ,

so mean is $50$%

$68$% of the distribution lies within one $Standard$ $Deviation$ d.

So, $68$% divided into $two$ parts :

$2d=68d=34$%

$m+d=50+34=84$%