brick2009 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?

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

Source---Princeton Review test...
OA: A

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A score of 440 is one unit of standard deviation below the mean in Group A, and the same score of 440 is two units of standard deviation below the mean in Group B. We want to know:
A: the % of data values that are more than 1 unit of standard deviation below the mean in a normal distribution
B: the % of data values that are more than 2 units of standard deviation below the mean in a normal distribution
The solution will be B/(A+B)

Now, what do we know about normal distributions? If you're studying to write the GMAT, you should know nothing about normal distributions, since the GMAT does not require test-takers to know how normal distributions behave (i.e., the % of values that lie a certain number of standard deviations above or below the mean). If you check the OG12, you'll see that "normal distribution" does not appear.

So, this question is out of scope.

I have a feeling that this is not a Princeton Review question.
For one, it's out of scope, but there are other problems with the question. For example, since there is (presumably) a finite number of students, the correct answer will be the closest approximation, not the exact value. Also, by my calculations, the answer is approximately 1/57

Takeaway: Be careful when examining posts. Some questions do not apply to the GMAT.

Brent is right: this question is way out of GMAT scope. I've posted elsewhere about the issues with the question; the source doesn't even give the right answer, for one thing (the correct answer is closer to 1/8 than to 1/9, though you need to consult a stats table to demonstrate that, something you clearly could never do on a GMAT). It also doesn't make any mathematical sense (finite sets cannot be normally distributed, though you don't need to know anything about this). The question is not only irrelevant to the GMAT, but it's poorly designed as well, as are similar questions from the same source. Best to move on!

Ian Stewart wrote:Brent is right: this question is way out of GMAT scope. I've posted elsewhere about the issues with the question; the source doesn't even give the right answer, for one thing (the correct answer is closer to 1/8 than to 1/9, though you need to consult a stats table to demonstrate that, something you clearly could never do on a GMAT). It also doesn't make any mathematical sense (finite sets cannot be normally distributed, though you don't need to know anything about this). The question is not only irrelevant to the GMAT, but it's poorly designed as well, as are similar questions from the same source. Best to move on!

Although this question is entirely out of scope, those who are perhaps learning about Normal distributions should know that the answer is, as Ian states, closer to 1/8 (and not 1/57)
Calculations: 0.0228/(0.0228+0.1587) = 1/8 (approx)
Serves me right for (poorly) using a calculator

brick2009 wrote:thanks Brent for the explanation and clarification...

This is one of the problems from the a PR-online test..that i have purchased.

Hi Brick,

That's quite surprising. Sorry for doubting the source - I wouldn't have guessed.

Cheers,
Brent