engg.manik wrote:Q.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%
We can use common sense to almost immediately eliminate A, B and C, even if we understand only a bit of the question.
We want to know what percent of the distribution is
less than m+d.
Well, since we have a symmetric distribution, roughly 50% of the distribution is less than m (I say roughly 50% because some of the distribution could be right on m); accordingly, more than 50% of the distribution is less than m+d, which is more than m. So, the answer must be either D or E.
To actually solve, we see that 68% of the data lie within 1 SD of the mean. So, 1 SD runs from 34% below the mean to 34% above the mean. 34% above the mean puts us at 84, so choose D.
If we want to be super picky, none of the answers are correct, since they're actually in the wrong format; the question says "what percent of...", so the right answer shouldn't have the percent sign included. Percent is a unit, just like miles or kilograms; if a question asked "how many miles did Bob travel", the answer would never be in the form of "50 miles" - it would simply be "50".
