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Two different groups of test-takers received scores on the

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Two different groups of test-takers received scores on the [#permalink] New post 22 Dec 2005, 20:44
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
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Re: Std Deviation [#permalink] New post 22 Dec 2005, 21:10
none...................

less than 440, group a = 68%/2 = 34%
less than 440, group b = 5%/2 = 2.5%

req % = 2.5%/36.5% = 1/14.6
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Std Deviation [#permalink] New post 22 Dec 2005, 21:13
Thanks for your response...however I have no idea how you calculated this. Further...I'm not even really sure what a standard deviation is other than knowing it has something to do with the distance from the mean. From reading the princeton review...I thought we wouldn't ever deal with these types of problems unless it was "how many std deviations away from this number is that number".
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 [#permalink] New post 22 Dec 2005, 23:04
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?

Answer is A

Assuming there are 100 people who took test A and 100 people who took test B.

Group A: 440 is 1 SD away from the mean, therefore, approx 16 ppl scored below 440 (Between 1 SD and the mean, percentage is roughly 34%)

Group B: 440 is 2 SDs away from the mean, therefore, approx 2 ppl scored below 440.

2/(16+2) = 2/18 ==> 1/9

Note: For a normal bell-curve distribution, between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%
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Last edited by TeHCM on 23 Dec 2005, 22:20, edited 1 time in total.
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Std Deviation [#permalink] New post 23 Dec 2005, 05:40
Quote:
Note: Between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%


Does this always hold true no matter what the standard deviation?

If the mean is 750 and the standard devation is 500, will approximately 34% of the people have scores between 250 and 750?
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 [#permalink] New post 23 Dec 2005, 07:31
TeHCM wrote:
Assuming there are 100 people who took test A and 100 people who took test B.

Group A: 440 is 1 SD away from the mean, therefore, approx 16 ppl scored below 440 (Between 1 SD and the mean, percentage is roughly 34%)

Group B: 440 is 2 SDs away from the mean, therefore, approx 2 ppl scored below 440.

2/(16+2) = 2/18 ==> 1/9

Note: Between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%

goodjob...............
i was lost here. i should have take 1-.68 = .32 or 32% instead 68/2=34%. i was looking for this but.........

anyway,
less than 440, group a = 32%/2 = 16%
less than 440, group b = 5%/2 = 2.5%

req % = 2.5%/18.5 = 1/9
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Re: Std Deviation [#permalink] New post 23 Dec 2005, 11:44
ellisje22 wrote:
Quote:
Note: Between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%


Does this always hold true no matter what the standard deviation?

If the mean is 750 and the standard devation is 500, will approximately 34% of the people have scores between 250 and 750?


Yes this always holds true for a normal distribution.

In this case, approx 34% scored between 750 - 1,250 and 250 - 750 or 68% who scored between 250 - 1250.
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Last edited by TeHCM on 23 Dec 2005, 22:58, edited 1 time in total.
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 [#permalink] New post 23 Dec 2005, 17:55
Thanks TechCM, for the lucid explanation.
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 [#permalink] New post 23 Dec 2005, 21:24
Thanks folks.....
I learnt a new concept in Standard Deviation today...

However I have few related questions...What are the other distributions (apart from Normal D mentioned in the question)........Does the same funda of 34%, 13.6% hold good for them as well...

Thanks in advance.
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 [#permalink] New post 23 Dec 2005, 22:30
Kishore wrote:
Thanks folks.....
I learnt a new concept in Standard Deviation today...

However I have few related questions...What are the other distributions (apart from Normal D mentioned in the question)........Does the same funda of 34%, 13.6% hold good for them as well...

Thanks in advance.


I've edited my previous post. The 68%-98% rule only applies to a normal distribution. I think its safe to say that only normal distributions will be tested on the GMAT.

Other distributions include bimodal, multimodal, J-curve...etc. And the 68%-98% rule does not apply.
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 [#permalink] New post 24 Dec 2005, 15:56
Thanx TeHCM.
It was a good tip for me. :-D


TeHCM wrote:
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?

Answer is A

Assuming there are 100 people who took test A and 100 people who took test B.

Group A: 440 is 1 SD away from the mean, therefore, approx 16 ppl scored below 440 (Between 1 SD and the mean, percentage is roughly 34%)

Group B: 440 is 2 SDs away from the mean, therefore, approx 2 ppl scored below 440.

2/(16+2) = 2/18 ==> 1/9

Note: For a normal bell-curve distribution, between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%
  [#permalink] 24 Dec 2005, 15:56
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