Problem Solving

The residents of the 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 hrs. The number of hrs that pat, a resident, watched television last week was between 1 and 2 standard deviation below the mean. which of the following could be the number of hours that pat watched television last week?

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

Can you please explain this?

The number of hrs that pat, a resident, watched television last week was between 1 and 2 standard deviation below the mean.

Is something missing here?

NO.. this is the exact question

g.shankaran wrote:The residents of the 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 hrs. The number of hrs that pat, a resident, watched television last week was between 1 and 2 standard deviation below the mean. which of the following could be the number of hours that pat watched television last week?

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

Can you please explain this?

Please correct me if I am wrong.

Here the SD is 6 and the mean = 21.

Pat watched television between 1 and 2 SD below mean. So assuming 1.5 SD, which is equal to 1.5 x 6 = 9. here the mean is 21. So the value could be 21-9 = 12.

In my view it is given that PAT has seen Television between 1 & 2 SD below mean which means:

As SD= 6 hrs(given)
1 SD= 6 hrs
2 SD= 12 hrs

Therefore its between 6 to 12 hrs below 21(mean)i.e between 9 hrs to 15 hrs

The only available option between 9 and 15 hrs is 12 hrs

Hence 12 is the answer

yes got it right guys 12 range : 9 to 15

g.shankaran wrote:The residents of the 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 hrs. The number of hrs that pat, a resident, watched television last week was between 1 and 2 standard deviation below the mean. which of the following could be the number of hours that pat watched television last week?

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

Can you please explain this?

This question is typical of the most common way the GMAT is currently testing standard deviation. All you need to solve is a very basic understanding of what SD is - the question itself is much simpler than it seems.

To solve quickly every time, draw a number line and put the mean in the middle:

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

Next, see if the question is asking for a number "below", "above" or "within" x standard deviations from the mean.

If "below", only worry about numbers below the mean.
If "above", only worry about numbers above the mean.
If "within", worry about numbers both below and above the mean.
(Questions can also ask about "from the mean", in which case you go below and above.)

This question asks for a number "between 1 and 2 standard deviation below the mean", so we work our way down from 21.

The SD is 6, so count off blocks of 6 to the left of the mean, 21:

-------3---------9----------15-----------21

Each number on the line represents 1 more SD below the mean. In other words:

15 is 1 SD below the mean;
9 is 2 SDs below the mean; and
3 is 3 SDs below the mean.

Since we want a number "between 1 and 2 standard deviation below the mean", any number between 9 and 15 fits the bill: choose (C)12.

If you understand how these questions work, they only take about 15 seconds to solve.