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A set has an average (arithmetic mean) of 42 and a standard deviation

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A set has an average (arithmetic mean) of 42 and a standard deviation [#permalink]

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New post 15 Aug 2016, 04:02
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Question Stats:

81% (00:34) correct 19% (00:45) wrong based on 96 sessions

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A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6
[Reveal] Spoiler: OA

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A set has an average (arithmetic mean) of 42 and a standard deviation [#permalink]

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New post 15 Aug 2016, 05:06
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6


AM is 42 and SD is 1.8...

Now, we need to count all numbers greater than 42+2(1.8) = 45.6 or 42-2(1.8) = 38.4 (we are asked to find the value that is two SD away from the mean..so multiply the SD by 2)

Only B is in the list..

IMO option B is correct answer..

OA please...will correct if I missed anything..

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Re: A set has an average (arithmetic mean) of 42 and a standard deviation [#permalink]

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New post 15 Aug 2016, 07:24
Expert's post
Top Contributor
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6


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, if the standard deviation is 1.8, then two standard deviations = (2)(1.8) = 3.6
So, two standard deviations BELOW the mean = 42 - 3.6 = 38.4
And two standard deviations ABOVE the mean = 42 + 3.6 = 45.6
This means there are two correct answers.
Now check the answer choices for one of the two possible answers.

Answer:
[Reveal] Spoiler:
B


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Re: A set has an average (arithmetic mean) of 42 and a standard deviation [#permalink]

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New post 13 Sep 2017, 08:47
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6


42-x= 2*1.8
x= 42-3.6 = 38.4

Ans:B

Kudos [?]: 13 [0], given: 85

Re: A set has an average (arithmetic mean) of 42 and a standard deviation   [#permalink] 13 Sep 2017, 08:47
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