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30 Nov 2004, 10:38
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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
a) 1/9
b) 1/8
c) 1/6
d) 4/17
e) 4/21
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30 Nov 2004, 10:55
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i suppose the right answer is A, but actually, the right answer is 5/37, which isn't up there.
This question is based on the known percentages of a normal distribution, and standard deviation. In group A, 16% of the test takers scored below 440, and in group b, 2.5% scored below 440. If we assume 100 students in each class, means 18.5 total scored below 440, so the answer is 2.5/18.5 = 5/37.
In the Princeton Review version of Standard Deviation, they ignore that .5% possibility for convenience sake, so in their world, Class B would have only 2% below 440, making the fraction 2 out of 18, or 1/9.
I don't know why the simplify things like that when it's wrong, but I guess it's a good way to make this stuff taste better to a large portion of their students.
At the same time, I haven't seen a GMAT question that actually required knowing those percentages, and I don't even teach them to my students, so I'm not sure this is even relevant.
Does that sound right?
This question is based on the known percentages of a normal distribution, and standard deviation. In group A, 16% of the test takers scored below 440, and in group b, 2.5% scored below 440. If we assume 100 students in each class, means 18.5 total scored below 440, so the answer is 2.5/18.5 = 5/37.
In the Princeton Review version of Standard Deviation, they ignore that .5% possibility for convenience sake, so in their world, Class B would have only 2% below 440, making the fraction 2 out of 18, or 1/9.
I don't know why the simplify things like that when it's wrong, but I guess it's a good way to make this stuff taste better to a large portion of their students.
At the same time, I haven't seen a GMAT question that actually required knowing those percentages, and I don't even teach them to my students, so I'm not sure this is even relevant.
Does that sound right?
30 Nov 2004, 11:17
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The problem says the values are normally distributed. Therefore 68% of all values fall within 1 standard deviation, 95% of all values fall within 2 standard deviations, and 99% of all values fall within 3 standard deviations.
Group A has a mean of 460 and a standard deviation of 20. So 1 standard deviation would be 440, so you are looking for values less than 440. Since you are dealing with only the left side of the curve you use 1/2 of 32 or 16%.
Group B has a mean of 520 and a standard deviation of 40. So it would take 2 standard deviations to get to 440 (520-80). Since you are dealing with the left side of the curve you use 1/2 of 5 or 2.5%.
Since you will be taking both 2.5% and 16% of a number use a number both go into like 400. 2.5% of 400=10 and 16% of 400=64. Since you can't have a fraction of a student and you want below scores of 440(not equal to them), use 9 and 63. Now you have 9/(63+9)=9/72=1/8. So the answer is B.
I had to look up the % tables and do a some calculations to get a number that worked well like 400. At first I got 5/37, but then I figured they wanted scores less than 440 so I decreased my values and ended up with an answer that was there. I really hope there isn't a question like this when I take the gmat.
Group A has a mean of 460 and a standard deviation of 20. So 1 standard deviation would be 440, so you are looking for values less than 440. Since you are dealing with only the left side of the curve you use 1/2 of 32 or 16%.
Group B has a mean of 520 and a standard deviation of 40. So it would take 2 standard deviations to get to 440 (520-80). Since you are dealing with the left side of the curve you use 1/2 of 5 or 2.5%.
Since you will be taking both 2.5% and 16% of a number use a number both go into like 400. 2.5% of 400=10 and 16% of 400=64. Since you can't have a fraction of a student and you want below scores of 440(not equal to them), use 9 and 63. Now you have 9/(63+9)=9/72=1/8. So the answer is B.
I had to look up the % tables and do a some calculations to get a number that worked well like 400. At first I got 5/37, but then I figured they wanted scores less than 440 so I decreased my values and ended up with an answer that was there. I really hope there isn't a question like this when I take the gmat.
), but you do not need to know anything about the properties of a normal distribution for the GMAT- and you definitely don't need to know what percentage of data points fall within one or two standard deviations in a normally distributed set of data. 
