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# A certain characteristic in a large population has a

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Manager
Joined: 17 Jan 2006
Posts: 92
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Kudos [?]: 3 [0], given: 0

A certain characteristic in a large population has a [#permalink]  30 Apr 2006, 19:33
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 ?

16%
32%
48%
84%
92%
Manager
Joined: 17 Jan 2006
Posts: 92
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Kudos [?]: 3 [0], given: 0

VP
Joined: 06 Jun 2004
Posts: 1059
Location: CA
Followers: 2

Kudos [?]: 47 [0], given: 0

Dinesh,

You can refer to my post here

http://www.gmatclub.com/phpbb/viewtopic ... 775#164775

and here

http://www.gmatclub.com/phpbb/viewtopic ... 199#176199

In a nutshell, 50% of the people would fall below and above the mean. And 68% of the people would fall within +/- 1 standard deviation of the mean. Therefore, 34% of the people would fall between m+d, and 34% would fall between m-d
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Director
Joined: 16 Aug 2005
Posts: 947
Location: France
Followers: 1

Kudos [?]: 10 [0], given: 0

It would be 68% + (100-68)/2 = 84%

Hence D
Manager
Joined: 27 Jan 2006
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Location: Europe
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Kudos [?]: 2 [0], given: 0

* i *
* i *
* i *
--(16)--*(34) ----M--- (34)*---(16)

16+34+34 = 84
Director
Joined: 04 Jan 2006
Posts: 926
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Kudos [?]: 16 [0], given: 0

i can try to explain.. I drew a diagram.. just a simple line to understand this..

--- means numbers in between.. m is mean, d is std deviation.

lowest--------m-d-------------m--------------m+d-------------------highest

so what we have is

lowest--------m-d-------------m--------------m+d-------------------highest
<-------------------------------------> is 68%
since we know they are symmetric about the mean, we have 50% before mean, and 50% after mean.
so we have:
lowest--------m-d-------------m--------------m+d-------------------highest
<-------------------------------------> is 68%
<--------------------------------><-------------------------------------------->
50% 50%
so now we know 32% below m-d or above m+d.. so now do the math.

68 + 16

84
which is 68 + 68-50
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