The residents of Town X participated in a survey to

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The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?

A. 30
B. 20
C. 18
D. 12
E. 6

[spoiler]OA=D[/spoiler]

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by Brent@GMATPrepNow » Sat Apr 06, 2019 6:38 am
Gmat_mission wrote:The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?

A. 30
B. 20
C. 18
D. 12
E. 6
---------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 distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?

So, 1 standard deviation BELOW the mean = 21 - 1(6) = 15
And 2 standard deviations BELOW the mean = 21 - 2(6) = 9

So, the number of hours that Pat watched television last week is BETWEEN 9 hours and 15 hours

Check the answer choices . . . . only answer choice D is BETWEEN 9 hours and 15 hours

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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