Standard Deviation Problem

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dreamzz2010: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Tue Sep 30, 2008 10:19 am

by dreamzz2010 » Fri Sep 25, 2009 4:48 pm

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

Please explain how did you get to the answer. Will post the answer shortly.

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Source: Beat The GMAT — Problem Solving | Fri Sep 25, 2009 4:48 pm

crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

Re: Standard Deviation Problem

by crackgmat007 » Fri Sep 25, 2009 10:10 pm

dreamzz2010 wrote: Please explain how did you get to the answer.

Key to solve the question is - normal distribution.
Check this site https://en.wikipedia.org/wiki/Normal_distribution

We need to find out how many test takers scored less than 440. We get 2% in for B & 16% (14 + 2) for A. Hence 2/16 = 1/8. Choose B.

HTH

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Fri Sep 25, 2009 11:43 pm

As I explained here:

www.beatthegmat.com/pr-4-standard-devia ... 16015.html

the above is a very poorly designed question. The answer they give isn't even correct; to do this kind of question accurately, you need to consult a stats table, and in their solution, they've used values which are rounded off. That rounding error actually leads them to choose answer A when answer B is much closer to the correct value.

In any case, you don't need to know anything about this for the GMAT, and you'd need a book of stats tables to be able to answer it with any precision; otherwise you'll likely make the same rounding error that the question designer made.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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dreamzz2010: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Tue Sep 30, 2008 10:19 am

by dreamzz2010 » Sat Sep 26, 2009 5:47 am

Thanks crackgmat007 and Ian for putting in your words.

I also found the question bit awkward and so wanted to know about the quality of question. I picked it up from one of the princeton tests anf the OA is 1/9.

Though i guess after reading Ian's comments no one would want to waste time on this one

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