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The arithmetic mean and standard deviation of a certain

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The arithmetic mean and standard deviation of a certain [#permalink]

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New post 15 Mar 2012, 08:29
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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
[Reveal] Spoiler: OA
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Re: The arithmetic mean and standard deviation of a certain [#permalink]

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New post 15 Mar 2012, 08:35
Expert's post
MaithiliGokarn 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

:|


The value which is exactly two SD less than the mean is: mean-2*SD=13.5-2*1.5=10.5.

Answer: A.

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Hope it helps.
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Re: The arithmetic mean and standard deviation of a certain [#permalink]

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New post 14 Dec 2017, 10:12
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Top Contributor
MaithiliGokarn 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


------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
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Re: The arithmetic mean and standard deviation of a certain   [#permalink] 14 Dec 2017, 10:12
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