stats - gmatprep - tv hours

arocks · Posted: Fri Oct 12, 2007 9:08 am Post subject: stats - gmatprep - tv hours

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 tv last week was between 1 and 2 standard deviations below mean.
Which of the following could be the number of hours that Pat watched tv last week?

A) 3
B) 20
C) 18
D) 12
E) 6

OA - D

Suyog · Posted: Fri Oct 12, 2007 10:36 am Post subject:

the mean is 21 and standard deviation is 6;
So the max hrs for which each resident watched the tv is 27 and min is 15 but since it is given that -

Standard deviation is between 1 and 2
so the way i calculated is: 6 * 1.5 = 9 i.e standard deviation.

standard deviations below mean.
as mean is 21.
The hrs for which Pat watched tv last week is 21 -9 = 12

I dont know if its the proper way of solving and i could make out only after i saw the answer.

ldoolitt · Posted: Fri Oct 12, 2007 3:06 pm Post subject:

The problem is testing your basic understanding of what a mean and standard deviation is.

Since the mean is 21 and the standard deviation is 6, 1 standard deviation below the mean would be 15 (21-6), and two standard deviations below would be 9 (21-2*6). Therefore the number of hours would have to be between 9 and 15. The only answer that fits that is 12, (D).

If you didn't know the definition of standard deviation and mean were, this would be a harder problem.