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# A certain characteristic in a large population has a

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Director
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A certain characteristic in a large population has a [#permalink]  04 Feb 2006, 14:57
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m+d?
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Re: stdev [#permalink]  04 Feb 2006, 15:04
joemama142000 wrote:
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m+d?

Not really sure I understand the question....I will go with 84%

50% are under mean m, and 34% are between m and one SD d
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Director
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i am not sure i understand at all?
Director
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oa is 84%. I dont understand either
VP
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joemama142000 wrote:
oa is 84%. I dont understand either

Okay.

In a normal bell curved distribution, 50% are below the mean and 50% are over it.

A total of 68% are distributed within 1 SDs of the mean ==> 34% are 1 SD above the mean and 34% are 1 SD below the mean.

You can find a more detailed explanation here

http://www.gmatclub.com/phpbb/viewtopic.php?p=165022
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VP
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Yep 84%.

100-68 = 32% lies in the region less than m-d and beyond m+d.

Also the distribution is symmetric about m. Hence 32/2 = 16% lies beyond m+d

Total less than m+d = 100-16 = 84%

Thanks for the pointer TeHCM.
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I don't think it must be normal bell distribution. This is another kind of distribution that maybe someone will find easier to understand!
Attachments

Distribution.JPG [ 39.03 KiB | Viewed 524 times ]

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VP
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thearch wrote:
I don't think it must be normal bell distribution. This is another kind of distribution that maybe someone will find easier to understand!

Hmmm, interesting...my stats teacher in college said that only applies to a normal bell-curve distribution.........Other distribution such as bimodal, J-curve, the percentages won't work.
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Distribution is symmetric around mean => 68/2 = 34% =>[mean-sd, mean] = [mean, mean+sd] = 34% So below mean+sd is 50+34 = 84%

Chirag
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here is my take

lets say m=10

what % lies under the mean? 50%

lets say one standard deviation from the mean d=5

m+d=15

therefore 84% below 15

-------5---------10----------15--------
(--16--)(--------68--------)(----16--)
VP
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joemama142000 wrote:
here is my take

lets say m=10

what % lies under the mean? 50%

lets say one standard deviation from the mean d=5

m+d=15

therefore 84% below 15

-------5---------10----------15--------
(--16--)(--------68--------)(----16--)

You got it
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