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]
Source: GMAT Prep
The residents of Town X participated in a survey to
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---------ASIDE--------------------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
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