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The arithmetic mean and standard deviation of a certain norm
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14 Sep 2020, 10:22
14 Sep 2020, 10:22
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The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5
Source: GMAT
A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5
Source: GMAT
Re: The arithmetic mean and standard deviation of a certain norm
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14 Sep 2020, 10:22
14 Sep 2020, 10:22
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: The arithmetic mean and standard deviation of a certain norm
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14 Sep 2020, 10:40
14 Sep 2020, 10:40
Carcass wrote:
The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5
Source: GMAT
A. 10.5
B. 11
C. 11.5
D. 12
E. 12.5
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.
------ONTO THE QUESTION!!!-----------------------------------
The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
2 standard deviations BELOW the mean = 13.5 - (2)(1.5)
= 13.5 - 3
= 10.5
= A
Cheers,
Brent
