Data Sufficiency

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% 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 standard deviation for the final exam was 10 points.

The OA is D. I am not sure I understand how we can answer the question with statement 1 alone. We need the standard deviation to determine how many scored higher than 96. Can someone please explain?

Vemuri 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% 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 standard deviation for the final exam was 10 points.

The OA is D. I am not sure I understand how we can answer the question with statement 1 alone. We need the standard deviation to determine how many scored higher than 96. Can someone please explain?

The question states that the scores have normal distribution with mean 76.

This means 50% of students scored above 76 and 50% scored below 76.

statement I

8 students received 96 or above

8 = x% 400

800/400 = x = 2

highest 2% received a score of 96 or above or remaining 48% students scored above 76 but below 96

In normal distribution, bottom 50% and above 50% are divided into 3 standard deviation

Mean to 1st SD = 34%
1st SD to 2nd SD = 14%
2nd SD to 3rd SD = 2%

Therefore, between 76 and 96 there are 2 standard deviations

76 + 2sd = 96

2sd = 96 - 76 = 20

sd = 10

1st SD - mean = 66 - 76 ----34%

2nd SD - 1st SD = 56 - 66 ---14%

3rd SD - 2rd SD = 56 and below ---2%


Hence 66 is the answer.

Hope this helps.

Great solution Morgoth! Is this question type likely to appear on the GMAT though? The standard deviation questions I've seen are far simpler than this one. This one requires that you know about normal distribution which I haven't seen in any of the study materials and really haven't seen since my business statistics class my sophomore year of college.

Thanks for your explanation Morgoth. Its made the concept very clear to me now.

Brent Hanneson wrote:

marcusking wrote:Great solution Morgoth! Is this question type likely to appear on the GMAT though? The standard deviation questions I've seen are far simpler than this one. This one requires that you know about normal distribution which I haven't seen in any of the study materials and really haven't seen since my business statistics class my sophomore year of college.

This question is out of scope; normal distributions are not tested on the GMAT.

This is very much a GMAT question. GMAT might not necessarily ask us to solve normal distribution questions, but it expects us to know the concept. BTW, this is a data sufficiency question, so we don't have to solve like Morgoth did (his explanation is more for our understanding), as long as we know the information provided in the statements are sufficient.

hai genial could u be able to answer this by using ND graph please.....