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# The arithmetic mean and standard deviation of a certain norm

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

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08 Mar 2010, 02:37
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88% (01:17) correct 12% (00:09) wrong based on 96 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-arithmetic-mean-and-standard-deviation-of-a-certain-129117.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Aug 2014, 04:28, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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08 Mar 2010, 08:23
1
KUDOS
Mean = 13.5
Two standard deviations is 1.5 + 1.5 = 3.0

There could be two calues for this.
Mean + two standard deviations = 16.5
Mean - Two standard deviations = 10.5

What is the OA?
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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08 Mar 2010, 08:28
ronny13 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 from the mean?

A) 10.5
B) 11
C) 11.5
D) 12
E) 12.5

Thanks

13.5-2(1.5) or 13.5_2(1.5)
10.5 or 16.5

hence A.
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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08 Mar 2010, 08:32
Agree with A

Two deviations in both directions : 13.5 + 2( 1.5) = 16.5

and 13.5 - 2(1.5) = 10.5
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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11 Jun 2011, 14:09
A..

It can be either 13.5 + 2(1.5) = 16.5

OR

13.5 - 2(1.5) = 10.5

Hence A
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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11 Jun 2011, 14:11
Why use the word "normal distribution " in the question? Does it add any meaning?
The question can be solved without it.

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

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11 Jun 2011, 16:47
puneetj wrote:
Why use the word "normal distribution " in the question? Does it add any meaning?
The question can be solved without it.

The word 'normal' could certainly be removed without changing the question in any way. The distribution doesn't need to have any special properties here.
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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11 Jun 2011, 17:37
AM = 13.5
SD = 1.5

the value that's 2 SD's away from the mean could be either 13.5+2(1.5) or 13.5-2(1.5)

i.e 13.5+3 or 13.5-3 = 16.5 or 10.5

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

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11 Jun 2011, 18:18
IanStewart wrote:
puneetj wrote:
Why use the word "normal distribution " in the question? Does it add any meaning?
The question can be solved without it.

The word 'normal' could certainly be removed without changing the question in any way. The distribution doesn't need to have any special properties here.

Thanks for the confirmation Ian
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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21 Aug 2014, 21:12
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Re: The arithmetic mean and standard deviation of a certain norm [#permalink]

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22 Aug 2014, 04:28
ronny13 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-arithmetic-mean-and-standard-deviation-of-a-certain-129117.html
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Re: The arithmetic mean and standard deviation of a certain norm   [#permalink] 22 Aug 2014, 04:28
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