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# The residents of Town X participated in a survey

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Manager
Joined: 24 Sep 2008
Posts: 167
Schools: MIT / INSEAD / IIM - ABC
The residents of Town X participated in a survey  [#permalink]

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01 Sep 2009, 15:11
3
20
00:00

Difficulty:

5% (low)

Question Stats:

82% (01:13) correct 18% (01:28) wrong based on 409 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 54434
Re: Statistics [Mean/Stnd Deviation] - GMAT Prep CAT1 (Hard one)  [#permalink]

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20 Dec 2010, 03:53
3
9
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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Re: Statistics [Mean/Stnd Deviation] - GMAT Prep CAT1 (Hard one)  [#permalink]

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01 Sep 2009, 16:19
3
3
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..
##### General Discussion
Senior Manager
Joined: 30 Aug 2009
Posts: 266
Location: India
Concentration: General Management

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02 Jan 2012, 06:58
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
Senior Manager
Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44
Re: The residents of Town X participated in a survey  [#permalink]

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22 Sep 2015, 01:03
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
Director
Joined: 04 Jun 2016
Posts: 564
GMAT 1: 750 Q49 V43
The residents of Town X participated in a survey  [#permalink]

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23 Jul 2016, 04:03
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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Re: The residents of Town X participated in a survey  [#permalink]

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13 Nov 2017, 01:23
i solved this using normal dist. method

mid value = 21
6 deviation to left = 21-6 = 15
12 deviation to left of 21 = 21-16 = 6

the value should be between 6 & 15 =12 hence D

kindly asses and revert, thanks.
Nisha
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Joined: 12 Sep 2015
Posts: 3587
Re: The residents of Town X participated in a survey  [#permalink]

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06 Apr 2019, 07:41
Top Contributor
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

---------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

Cheers,
Brent

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Re: The residents of Town X participated in a survey   [#permalink] 06 Apr 2019, 07:41
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