The residents of Town X participated in a survey :: Manhattan GMAT Forums

Posted: Fri May 16, 2008 2:15 pm

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

I got the range for the Town X (15 to 27) and Pat's is (19-21). I picked "B", but the correct answer is D. I realize that I am not using all of the information that is given, therefore my approach is wrong. What is the right approach for this problem? Please help.

Posted: Fri May 16, 2008 9:33 pm

Average(mean) for the town = 21 h
Standard deviation for the town = 6 h

Pat was between 1 and 2 standard deviations below the mean.

One standard deviation below the mean = Mean - 1*SD = 21 - 6 = 15 h

Two standard deviations below the mean = Mean - 2*SD = 21 - 2(6) = 21 - 12 = 9 h

Therefore, the correct answer (the numbers of hours Pat watched television) lies between 9 and 15 h.

The only correct answer that satisfies that condition is D (12 h).

BI

Posted: Sun May 18, 2008 12:48 pm

I see now. Thanks for taking your time.

Posted: Fri May 23, 2008 3:22 am

Paul 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

I got the range for the Town X (15 to 27) and Pat's is (19-21). I picked "B", but the correct answer is D. I realize that I am not using all of the information that is given, therefore my approach is wrong. What is the right approach for this problem? Please help.

when you see a problem like this one, the key is to realize that you are really NOT being tested on anything that has to do with the actual meaning of the standard deviation. instead (and ironically), you should basically try to ignore the significance of the term 'standard deviation' entirely in this problem. for instance, let's say i gave you the following:
jimmy ate 33 hot dogs in an eating contest, and there are 8 hot dogs in a pack. if wes ate between 1 and 2 packs fewer than jimmy did, then how many hot dogs could wes have eaten?
you'd almost certainly have very little trouble with this version: the answer is between 33 - 2(8) and 33 - 8, or between 17 and 25.
same thing here: the answer is between 21 - 2(6) and 21 - 6, or between 9 and 15.

--

p.s. 21 hours of tv per week on average? dear god.