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by ruplun » Mon May 09, 2011 5:25 am
At Rocktown college , the 400 students taking Psychology 101 received an average score of 76 on the final exam, and the scores had a normal distribution.The bottom 16 percent of scores will receive a failing grade.What is the score at or below which students fail the course?

(1) 8 students receive a score of 96 or higher.
(2) The SD for the final exam was 10 points.

I found the ans to be B , but in the ans option its given D .Please explain ...
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by Brent@GMATPrepNow » Mon May 09, 2011 8:30 am
ruplun wrote:At Rocktown college , the 400 students taking Psychology 101 received an average score of 76 on the final exam, and the scores had a normal distribution.The bottom 16 percent of scores will receive a failing grade.What is the score at or below which students fail the course?

(1) 8 students receive a score of 96 or higher.
(2) The SD for the final exam was 10 points.

I found the ans to be B , but in the ans option its given D .Please explain ...
This question is out of scope for the GMAT, since it requires you to know about normal distributions (you will find no mention of "normal distributions" in the Official Guide for the GMAT)

Cheers,
Brent
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by pemdas » Mon May 09, 2011 8:43 am
The standard deviation is a statistically derived specified distance from the mean. On GMAT we will never have to calculate the standard deviation from the data alone. GMAT problems will tell us the standard deviation for a set of data. However, we could memorize percentages 34: 14 : 2 (%) which correspond to the 1st, 2nd, and 3rd standard deviations on each side of the mean.

st(1) 8 students out of 400 makes 2%. So 2% will receive a score of 96 or higher. Our average score is 76, therefore one standard deviation in the score distribution corresponds to (96-76)/2=10 points/score {the score of 96 is one standard deviation to the left from the mean/average, 2%). Two standard deviations in the scores to the right from the mean/average will make 76 {average/mean} - 2*10 or 56. Sufficient, as we can answer the score at or below which students fail the course is 56.

st(2) standard deviation is given =10 points. The same way as in statement (1) BUT we know the average from the question itself 76-2*10=56 Sufficient

IOM d
ruplun wrote:At Rocktown college , the 400 students taking Psychology 101 received an average score of 76 on the final exam, and the scores had a normal distribution.The bottom 16 percent of scores will receive a failing grade.What is the score at or below which students fail the course?

(1) 8 students receive a score of 96 or higher.
(2) The SD for the final exam was 10 points.

I found the ans to be B , but in the ans option its given D .Please explain ...
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by pemdas » Mon May 09, 2011 8:44 am
the question is 100% within the scope of GMAT is rated 500-level difficulty. I've been coached by GMAT tutor who assured me about this. Normal distribution is just a term to signal about the use of standard deviation problem type on GMAT-no other statistical parameters related to the normal distribution are expected to be tested on exam.
Brent@GMATPrepNow wrote:
ruplun wrote:At Rocktown college , the 400 students taking Psychology 101 received an average score of 76 on the final exam, and the scores had a normal distribution.The bottom 16 percent of scores will receive a failing grade.What is the score at or below which students fail the course?

(1) 8 students receive a score of 96 or higher.
(2) The SD for the final exam was 10 points.

I found the ans to be B , but in the ans option its given D .Please explain ...
This question is out of scope for the GMAT, since it requires you to know about normal distributions (you will find no mention of "normal distributions" in the Official Guide for the GMAT)

Cheers,
Brent
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