Problem Solving

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%

Not sure , i am taking a hit .

If 68 % fall within one standard deviation means 32 % are outside this . Since its symmetric around mean , so 32/2 = 16 % would be outside m + d .

Where did u get the 6 from?

Sorry for the typo . I meant 2 instead of 6 . Have corrected it .

I see it as this. Say 100 people take the test and the mean is 50 (m=50). 34 (d) people had more than 50, 34 had less than 50 (symmetrical 34 and 34 = 68). What percent of people would be less than m+d or 34+50. I think D 84%

it is 50+34 = 84%

In normal distributoin 50% below the mean and 50% above.
m+d = 34%, m+2d = 14% m+3d = 2%

m-d = 34%, m-2d = 14% m-3d = 2%

here above m+d is 14+2 = 16%

it is 50+34 = 84%

In normal distributoin 50% below the mean and 50% above.
m+d = 34%, m+2d = 14% m+3d = 2%

m-d = 34%, m-2d = 14% m-3d = 2%

"here above m+d is 14+2 = 16%"

Where did u get m+d=14+2?

rohan_vus wrote:Not sure , i am taking a hit .

If 68 % fall within one standard deviation means 32 % are outside this . Since its symmetric around mean , so 32/2 = 16 % would be outside m + d .

It is B - 32%. You don't need to divide by 2. m+d is on both sides.

so is it 16 or 32?

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%

Apparently the OA is D.

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".