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A certain characteristic in a large population has a distrib

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by Max@Math Revolution » Sun Jul 15, 2018 11:58 pm

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[GMAT math practice question]

A certain characteristic in a large population has a distribution that is symmetric about the mean m. 68 percent of the distribution lies within one standard deviation d of the mean. The average score of students in a certain class is 72 pts. 84% of students in the class score less than 80 pts. What is the standard deviation of the students' scores?

A. 1
B. 2
C. 4
D. 8
E. 16
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by swerve » Mon Jul 16, 2018 9:28 am
Given, 84% of the students in the class score less than 80 pts.

In the standard normal distribution curve, region of 84% students lies to the left of (m+d), where m=mean, d=standard deviation.

Given, m=72, we have m+d=80.

Or, 72+d=80

Or, d=80-72=8.

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by Max@Math Revolution » Wed Jul 18, 2018 3:48 am
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80 - 72 = 8 is the standard deviation of the distribution.


Therefore, D is the answer.

Answer: D
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Re: A certain characteristic in a large population has a distrib

by Scott@TargetTestPrep » Sat Mar 21, 2020 2:42 pm
Max@Math Revolution wrote: ↑
Sun Jul 15, 2018 11:58 pm
 [GMAT math practice question]

A certain characteristic in a large population has a distribution that is symmetric about the mean m. 68 percent of the distribution lies within one standard deviation d of the mean. The average score of students in a certain class is 72 pts. 84% of students in the class score less than 80 pts. What is the standard deviation of the students' scores?

A. 1
B. 2
C. 4
D. 8
E. 16
Since the distribution is symmetric, 50 percent of the data points in the distribution are less than m and 68/2 = 34 percent of the data points in the distribution are between m and m + d. Therefore, a total of 50 + 34 = 84 percent of the data points in the distribution are less than m + d.

Answer: D

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