The residents of Town X participated in a survey to determine the numb

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

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

Bunuel · Accepted Answer

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.

Answer: D.

gmate2010 · Answer

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..

Now, about the problem, 
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..

kp1811 · Answer

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

TeamGMATIFY · Answer

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

LogicGuru1 · Answer

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 
ANSWER IS D

nishasharmagsk · Answer

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

BrentGMATPrepNow · Answer

---------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    9  + 2( 4 ) =  17 ]  
1.5 standard deviations BELOW the mean =  3    9  - 1.5( 4 ) =  3 ]  
3 standard deviations ABOVE the mean =  21    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

sanjeevsinha082 · Answer

1 and 2 standard deviations below the mean=>number of the hours at most is 21-6=15, at least 
is 21-2*6=9. 
Average of the sum of the squared differences:
770
21 = 36
2
3Answer is D

eega · Answer

Given mean = 21 & SD = 6
Hence 1 & 2 SD below mean indicate the number is between 21-6 & 21-12 --> 15 to 9
Hence its  Option D

The residents of Town X participated in a survey to determine the numb

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