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statistics - mean and standard deviation

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statistics - mean and standard deviation [#permalink]  28 May 2007, 15:13
question :
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a norrmal distribution with a mean of 460 and standard deviatiation of 20. Group B's scores had a norrmal distribution with a mean of 520 and standard deviatiation of 40. If each group has the same number of test takers, what fraction of the test-takers whos scored below 440 belonged to group B.

a. 1/9
b. 1/8
c. 1/6
d. 4/17
e. 4/21
Director
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Re: statistics - mean and standard deviation [#permalink]  28 May 2007, 18:44
mpjena wrote:
question :
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a norrmal distribution with a mean of 460 and standard deviatiation of 20. Group B's scores had a norrmal distribution with a mean of 520 and standard deviatiation of 40. If each group has the same number of test takers, what fraction of the test-takers whos scored below 440 belonged to group B.

a. 1/9
b. 1/8
c. 1/6
d. 4/17
e. 4/21

in first case, the area below 1 SD from the mean = (100% - 68%)/2= 16%
in second case, the area below 2 Sd is = (100% - 95%)/2= 2.5%

so the fraction = 2.5%/(16%+2.5%) = 2.5/18.5 = close to 1/8. since 1/9 and 1/8 are close to each other, could be 1/9.
Senior Manager
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The same logic as Himalayan has. I would chose 1/8.
25/185=5/37, which is close to 1/8

Maybe someone can solve it in another way?
Manager
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I'm in agreement with Caas. I think the answer is really close to 1/8
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Re: statistics - mean and standard deviation [#permalink]  29 May 2007, 10:31
Himalayan wrote:
mpjena wrote:
question :
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a norrmal distribution with a mean of 460 and standard deviatiation of 20. Group B's scores had a norrmal distribution with a mean of 520 and standard deviatiation of 40. If each group has the same number of test takers, what fraction of the test-takers whos scored below 440 belonged to group B.

a. 1/9
b. 1/8
c. 1/6
d. 4/17
e. 4/21

in first case, the area below 1 SD from the mean = (100% - 68%)/2= 16%
in second case, the area below 2 Sd is = (100% - 95%)/2= 2.5%

so the fraction = 2.5%/(16%+2.5%) = 2.5/18.5 = close to 1/8. since 1/9 and 1/8 are close to each other, could be 1/9.

How can you divide the percentages. It should be 2.5% of 520/(16%of 460+ 2.5% of 520) = 13/87
The closest is 1/6
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Re: statistics - mean and standard deviation [#permalink]  29 May 2007, 10:48
vshaunak@gmail.com wrote:
Himalayan wrote:
mpjena wrote:
question :
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a norrmal distribution with a mean of 460 and standard deviatiation of 20. Group B's scores had a norrmal distribution with a mean of 520 and standard deviatiation of 40. If each group has the same number of test takers, what fraction of the test-takers whos scored below 440 belonged to group B.

a. 1/9
b. 1/8
c. 1/6
d. 4/17
e. 4/21

in first case, the area below 1 SD from the mean = (100% - 68%)/2= 16%
in second case, the area below 2 Sd is = (100% - 95%)/2= 2.5%

so the fraction = 2.5%/(16%+2.5%) = 2.5/18.5 = close to 1/8. since 1/9 and 1/8 are close to each other, could be 1/9.

How can you divide the percentages. It should be 2.5% of 520/(16%of 460+ 2.5% of 520) = 13/87
The closest is 1/6

No. We are asked to solve for the fraction of students.
In your solution you mix up students with scores.
Manager
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how frequent are these sorts of questions? i don't mind them per se, as statistics was one of my favorite subjects... i am able to hit the ground running with them..but i am not looking forward to a q where i have to actually compute the SD from a table of data. it just takes too long IMHO....
Manager
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Yeah Caas! I was worried for a second that my answer was incorrect. Good observation of that error.
Senior Manager
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Anybody knows why 1/9?
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