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Two different group of test takers received scores on the

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Intern
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Two different group of test takers received scores on the [#permalink]

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New post 06 Aug 2008, 17:45
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Two different group of test takers received scores on the GYZ test. Group A had a normal distribution with mean of 460 and a Standard Deviation of 20. Group B had a normal distribution with mean of 520 and a Standard Deviation of 40. If each group has the same number of test takers, what fractio of test takers who scored below 440 belong to Group B ??

1/9

1/8

1/6

4/17

4/21.

Please help solve this...

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Director
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Re: Standard Deviation and Normal Distribution [#permalink]

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New post 06 Aug 2008, 18:02
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Guessing 4/21

this is somewhat of a convoluted question.

approx 68% falls between 1 SD of the average, so 32% outside of 1SD from average.
approx 95% falls between 2 SD of the average, so 5% outside of 2SD from average.

lets say 100 people in each group

in group A 16 people will be below 1 SD from average (32/2)

in group B 2.5 people will be below 2 SD from average (5/2)

So about 18.5 people (16 + 2.5) score lower than 440 from both groups

2.5/18.5 is somewhat closer to E than it it to D

not completely sure about my approximation.

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Re: Standard Deviation and Normal Distribution [#permalink]

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New post 06 Aug 2008, 19:13
i think A..
the logic as above is same,..
but i have got my result on the basis that 68% is within the 1 st deviation
28% next , and 4% on the last..
BTW, what is the correct values.?
some books say 68%,28%,4%
others say 68, 27,and 5... :roll:

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Re: Standard Deviation and Normal Distribution [#permalink]

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New post 08 Aug 2008, 09:11
hello... can the einsteins pitch in???

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Re: Standard Deviation and Normal Distribution [#permalink]

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New post 08 Aug 2008, 10:13
First ot all i dont think its a GMAT question.. we are not supposed to know the properties of normal distribution..

i agree with gmatnub's approach .. the answer should be 2.5/18.5 actually 2.2/18 to be more accurate

closest option is B 1/8.

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Re: Standard Deviation and Normal Distribution [#permalink]

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New post 08 Aug 2008, 17:17
I haven't even read the question (but I trust Durgesh :) ), but you do not need to know anything about the properties of a normal distribution for the GMAT- and you definitely don't need to know what percentage of data points fall within one or two standard deviations in a normally distributed set of data.
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Re: Standard Deviation and Normal Distribution [#permalink]

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New post 08 Aug 2008, 17:23
IanStewart wrote:
I haven't even read the question (but I trust Durgesh :) ), but you do not need to know anything about the properties of a normal distribution for the GMAT- and you definitely don't need to know what percentage of data points fall within one or two standard deviations in a normally distributed set of data.


I am not sure about to what extent we need to understand these properties, but it won't harm if we remember these properties as well.
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Re: Standard Deviation and Normal Distribution   [#permalink] 08 Aug 2008, 17:23
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