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# The residents of Town X participated in a survey

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The residents of Town X participated in a survey [#permalink]

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01 Sep 2009, 14:11
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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
[Reveal] Spoiler: OA
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Re: Statistics [Mean/Stnd Deviation] - GMAT Prep CAT1 (Hard one) [#permalink]

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01 Sep 2009, 15:19
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First of all,I would suggest you to go through some documentation about means, medians, mode, standard deviations etc..It is good to know some theory as well..

Given, Mean = 21 ; S.D = 6

Now, any value which is 1 standard deviation above the mean is = mean + S.D = 21 + 6 = 27

any value which is 1 standard deviation below the mean is = mean - S.D = 21 - 6 = 15

any value which is 2 standard deviation above the mean is = mean + 2* S.D = 21 + 2*6 = 33

any value which is 2 standard deviation below the mean is = mean - 2* S.D = 21 - 2*6 = 9

question is asking for that value which is between 1 and 2 S.D below the mean..i.e. between 9 and 15

only 12 lies between 9 and 15.. hence, the answer is 12..
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Re: Statistics [Mean/Stnd Deviation] - GMAT Prep CAT1 (Hard one) [#permalink]

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20 Dec 2010, 02:53
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thangvietnam wrote:
I CAN NOT READ THE QUESTION. PLEASE, POST IT CLEARLY. GMATPREP QUESTIONS IS GOOD ONES TO STUDY

You should click the image to zoom in. Anyway here is the question:

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

Given: mean=21 and SD=6.

The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean is mean-1*SD=15 and 2 SD below the mean is mean-2*SD=9, so the number of hours that Pat watched television was between 9 and 15 hours.

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02 Jan 2012, 05:58
Mean is 21 hours and SD is 6hours

Kotela watched television 1-2 SD below Mean -> which means that Kotela watched television 12 to 6 hours below Mean of 21hours

so number of hours will be between 21-12 & 21 -6 = 9 and 15. Only D - 12 satisfies
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Re: The residents of Town X participated in a survey [#permalink]

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16 Aug 2014, 11:21
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Re: The residents of Town X participated in a survey [#permalink]

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21 Sep 2015, 19:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The residents of Town X participated in a survey [#permalink]

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22 Sep 2015, 00:03
The standard deviation is simply the distance a value is away from the mean of the set.
In this case, SD = 6 and the mean = 21

Hence one 1 SD value below the mean = 15 and two SD values below the mean = 9
We need to find the value that falls between 9 and 15.

Going through the options, only one value satisfies this. Option D:12
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The residents of Town X participated in a survey [#permalink]

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23 Jul 2016, 03:03
GODSPEED 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

Mean =21 ; SD= 6
Mean -1 SD= 21-6=15
Mean-2SD - 21- 12 = 9

Range {From 1 SD to 2SD} = 9 to 15
What value lies between 9 to 12 that matches our options ===> 12
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The residents of Town X participated in a survey   [#permalink] 23 Jul 2016, 03:03
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