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500 records have a distribution that is symmetric about the

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500 records have a distribution that is symmetric about the [#permalink]

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New post 03 Nov 2008, 01:21
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500 records have a distribution that is symmetric about the mean 10. If 68% of the distribution lies within one standard deviation of the mean and the deviation is 2, then atleast how many of the records are less than 12?

A-160
B-320
C-340
D-420
E-460

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Re: PS - statistics [Good one] [#permalink]

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New post 03 Nov 2008, 02:10
is it A ?
Normally i would spend just 1 minute in these kind of qs, because i am never too sure of them, hence i would calculate as little as possible and make an educated guess.
In this, its mentioned that 68 % of 500 records are within SD of 2 from mean 10 i.e. either 8 or 12. So lets assume its on positive side of 10 which is 12, so 32% will be on lower side of 10. Hence the least number of records with less than 12 mean will be 32% of 500 which is 160.

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Re: PS - statistics [Good one] [#permalink]

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New post 03 Nov 2008, 02:36
D.

percentage beyond +- 1sd = 100-68 = 32% and hence % before -1sd = 16%.

Thus, total percentage before mean + 1sd = 16 + 68 = 84% and 84% of 500 is 420.

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Re: PS - statistics [Good one] [#permalink]

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New post 03 Nov 2008, 02:42
C.
IMO. in order to get min. the records more than 12 must be max, which could be 32%.
The given 68% could be min below 12 ,because 68% lies between 8-12). 68%*500=340

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Re: PS - statistics [Good one] [#permalink]

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New post 03 Nov 2008, 03:57
scthakur wrote:
D.

percentage beyond +- 1sd = 100-68 = 32% and hence % before -1sd = 16%.

Thus, total percentage before mean + 1sd = 16 + 68 = 84% and 84% of 500 is 420.


scthakur can you elaborate your approach ....
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Re: PS - statistics [Good one] [#permalink]

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New post 03 Nov 2008, 10:58
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amitdgr wrote:
scthakur wrote:
D.

percentage beyond +- 1sd = 100-68 = 32% and hence % before -1sd = 16%.

Thus, total percentage before mean + 1sd = 16 + 68 = 84% and 84% of 500 is 420.


scthakur can you elaborate your approach ....


This is a normal distribution case. Sorry for not having the drawing. But, if you draw a normal distribution curve, the area with mean+1sd and mean-1sd will be 68%. HEnce, the remaining area outside of mean+1sd and mean-1sd will be 32% and half of it will be to the left of mean-1sd.

Thus, total area to the left of mean+1sd = 32/2 + 68 = 84%.

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Re: PS - statistics [Good one] [#permalink]

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New post 04 Nov 2008, 16:13
Thank you scthakur :)
I learnt something

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Re: PS - statistics [Good one] [#permalink]

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New post 04 Nov 2008, 17:36
Also what is important is that the distribution is symmetrical about the mean. Thus 100-68 = 32% is evenly split between values above 12 and below 8. If the distribution were not symmetrical, we cannot obtain 68+16 = 84%

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Re: PS - statistics [Good one]   [#permalink] 04 Nov 2008, 17:36
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500 records have a distribution that is symmetric about the

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