Problem Solving

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?

Answer Optioons:

1. 30
2. 20
3. 18
4. 12
5. 6

4


21 - 6 = 15 = 1 standard deviation

21 - 12 = 9 = 2 standard deviation

only number between 9 and 15 = 12

This is pretty straightforward. Tests your understanding that 1 and 2 standard deviations below the mean means mean-2sd < x < mean-1sd.

The correct answer is D. This is QID 1443

-Patrick

sp.wonder2010 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?

Answer Optioons:

1. 30
2. 20
3. 18
4. 12
5. 6

This is the most common way in which standard deviation is currently tested on the GMAT, so it's a great question to post and discuss.

Many people find that the quickest way to solve these problems is to plot the distribution on the number line. Start with the mean:

------------------------------------------------21----------------------------------------------

Next, count off to the left and right of the mean intervals equal to the standard deviation (on this question we'd only count off below 21, since that's what the question asks, but other variations have asked "between 1 and 2 standard deviations from the mean", so we could go in either direction):


-----3--------9-------15----------21----------27-----------33------------39

Finally, plot your point on the number line. We want "between 1 and 2 standard deviations below the mean"; so, counting to the left of 21, we have "15", 1 SD below the mean, and "9", 2 SDs below the mean. Accordingly, the correct answer must be between 9 and 15: choose (4).

If you use this approach, this type of question will take 15-20 seconds to answer.