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For a certain exam, a score of 58 was 2 standard deviations
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14 Sep 2020, 10:27
14 Sep 2020, 10:27
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For a certain exam, a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?
A. 74
B. 76
C. 78
D. 80
E. 82
Source: GMAT
A. 74
B. 76
C. 78
D. 80
E. 82
Source: GMAT
Re: For a certain exam, a score of 58 was 2 standard deviations
[#permalink]
14 Sep 2020, 10:27
14 Sep 2020, 10:27
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Posts: 6218
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Re: For a certain exam, a score of 58 was 2 standard deviations
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14 Sep 2020, 10:38
14 Sep 2020, 10:38
3
Carcass wrote:
For a certain exam, a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?
A. 74
B. 76
C. 78
D. 80
E. 82
Source: GMAT
A. 74
B. 76
C. 78
D. 80
E. 82
Source: GMAT
----------ASIDE---------------------
A little extra background on standard deviations above and below the mean
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-------------------------------------------------------------
For this question, we can let M=mean and let D=the standard deviation
So, 58 is 2 standard deviations below the mean translates into M - 2D = 58
and 98 is 3 standard deviations above the mean translates into M + 3D = 98
When we solve this system of equations, we get M=74 and D=8
So the answer is A
Cheers,
Brent
