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aiming4mba
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PS Question 01 Sep 2010, 11:12
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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



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Bunuel
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PS Question 01 Sep 2010, 11:52
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aiming4mba
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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You can solve this question if you know the 68.2-95.4-99.7 rule of normal distributions. But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.
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PS Question 01 Sep 2010, 12:21
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Not sure if it is a GMAT question but...



Assuming that each group has 100 test-takers, from the distribution above we see that there are 15,8 test-takers scored below 440 in group A and 2,2 in group B = 15,8 + 2,2 = 18.

So the fraction of the test takers that belonged to B and scored below 440 is: 2,2/18 = 1,1/9 (choice A)
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PS Question 01 Sep 2010, 12:42
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MBAUncle
Not sure if it is a GMAT question but...



Assuming that each group has 100 test-takers, from the distribution above we see that there are 15,8 test-takers scored below 440 in group A and 2,2 in group B = 15,8 + 2,2 = 18.

So the fraction of the test takers that belonged to B and scored below 440 is: 2,2/18 = 1,1/9 (choice A)
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As I mentioned this is not realistic GMAT question. Moreover answer A(1/9) is wrong, actual answer is closer to 1/8 than to 1/9.

Approximate ratio is \(\frac{2.2}{18}=0.1(2)\) --> \(\frac{1}{8}=0.125\) and \(\frac{1}{9}=0.(1)\), you can see that 1/8 is closer to the ratio than 1/9.
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PS Question 01 Sep 2010, 14:12
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Bunuel
MBAUncle
Not sure if it is a GMAT question but...



Assuming that each group has 100 test-takers, from the distribution above we see that there are 15,8 test-takers scored below 440 in group A and 2,2 in group B = 15,8 + 2,2 = 18.

So the fraction of the test takers that belonged to B and scored below 440 is: 2,2/18 = 1,1/9 (choice A)

As I mentioned this is not realistic GMAT question. Moreover answer A(1/9) is wrong, actual answer is closer to 1/8 than to 1/9.

Approximate ratio is \(\frac{2.2}{18}=0.1(2)\) --> \(\frac{1}{8}=0.125\) and \(\frac{1}{9}=0.(1)\), you can see that 1/8 is closer to the ratio than 1/9.
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Very well noted Bunuel ! In this case I would have missed this question. :oops:
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PS Question 01 Sep 2010, 15:54
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As Bunuel pointed out, normal distribution is not a topic that's tested on the GMAT. :) (MBAuncle - you'll be fine, don't worry) :D
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PS Question 01 Sep 2010, 23:09
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Thanks bunuel... you are life saver...ha...ha.



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