A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 84 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? Choose the correct choice from the following answers.
A) 16% B) 32% C) 48% D) 84% E) 92%
This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.   So, if 84% is one st.Dev, then on either side of m we have  84/2= 
<gadget id="calculator"> 84/2</gadget>
<output>42</output>
42%. So, 84% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 42= 
<gadget id="calculator">50 + 42</gadget>
<output>92</output>
92% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 92% of the values are below m + d.   Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it   92%
<result>E</result>
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 84 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?