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# The arithmetic mean and standard deviation of a certain

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Intern
Joined: 20 Nov 2011
Posts: 2
The arithmetic mean and standard deviation of a certain  [#permalink]

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15 Mar 2012, 07:29
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5% (low)

Question Stats:

91% (00:34) correct 9% (00:46) wrong based on 344 sessions

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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
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Joined: 02 Sep 2009
Posts: 64144
Re: The arithmetic mean and standard deviation of a certain  [#permalink]

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15 Mar 2012, 07:35
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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.

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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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14 Dec 2017, 09:12
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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]

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11 Oct 2019, 07:49
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

13.5 - 2*1.5

= 10.50 , Answer must be (A)
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Re: The arithmetic mean and standard deviation of a certain  [#permalink]

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02 Apr 2020, 10:09
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

Two standard deviations less than the mean is 13.5 - 2 x 1.5 = 13.5 - 3 =10.5.

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Re: The arithmetic mean and standard deviation of a certain   [#permalink] 02 Apr 2020, 10:09