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Two different groups of test-takers received scores on the [#permalink]
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?

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".

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% _________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Last edited by TeHCM on 23 Dec 2005, 22:20, edited 1 time in total.

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 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. _________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

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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