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# Two different groups of test-takers received scores on the

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Manager
Joined: 19 Jun 2003
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Two different groups of test-takers received scores on the [#permalink]  06 Nov 2004, 22:07
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Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B's scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

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

GMAT Club Legend
Joined: 15 Dec 2003
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I'd say B) 1/8
This is certainly not a GMAT problem as it has to do with normal distribution and z-scores
68% of results are within 1 SD
95% of results are within 2 SD
A) within 1 SD so 16% below 1 SD of 440
B) within 2 SD so approx 2% below 2 SD of 440
2/16 = 1/8
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Paul

Director
Joined: 16 Jun 2004
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Pls refer to my diagram in http://www.gmatclub.com/phpbb/viewtopic ... stribution

You'll understand what Paul is referring to.
Manager
Joined: 19 Jun 2003
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OA is different.

It is PR gmat cat (online) question..
GMAT Club Legend
Joined: 15 Dec 2003
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hmmm, I would suspect this kind of question be on the GMAT though. The exact answer should be something like 2.28/15.87 = 14.37% which is closer to 1/7 but it is not among the answer choices. I believe you have to refer to a z-table...
Check out this site to just plug in the values for the z-distribution
http://davidmlane.com/hyperstat/z_table.html
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Best Regards,

Paul

Senior Manager
Joined: 19 May 2004
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As Paul said,
A) within 1 SD so 16% below 1 SD of 440
B) within 2 SD so approx 2% below 2 SD of 440

But notice that the TOTAL % of people in both groups who are below 440,
Is actually 16/2+2/2=9%.

(2/2) / 9 = 1/9.

So the answer should be A.
Senior Manager
Joined: 19 Oct 2004
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Location: Missouri, USA
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Dookie wrote:
As Paul said,
A) within 1 SD so 16% below 1 SD of 440
B) within 2 SD so approx 2% below 2 SD of 440

But notice that the TOTAL % of people in both groups who are below 440,
Is actually 16/2+2/2=9%.

(2/2) / 9 = 1/9.

So the answer should be A.

hi,

can u please explain the second part of your calculation?? I couldnt understand it.

Your help will be appreciated. Thanks.
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Let's get it right!!!!

Senior Manager
Joined: 19 May 2004
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Sure,

Each group has the same number of people in it.
So A=B and A+B=100%
The 9% of the TOTAL consists of 2 % of the first half (B), and 16% of the second half of the group (A).
2% of B, is actually only 1% of the total (A+B).
16% of A, is actually only 8% of the total (A+B).
Together they are 1+8=9% of the total.
of it, 1% belongs to B.

So, 1/9.

I hope i manged to explain it
GMAT Club Legend
Joined: 15 Dec 2003
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Agree with 1/9 Dookie. The catch in this problem was that you had to add the two parts to make the whole and hence the answer. Thanks Dookie!
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Best Regards,

Paul

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