Standard Deviation

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k_suraj786: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Apr 22, 2006 8:49 am; Location: Mumbai

by k_suraj786 » Sat Apr 22, 2006 9:15 am

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 ?

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

Could somebody help me out at Standard Deviation stuff......I really dont figure this out...?

SKK

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Source: Beat The GMAT — Problem Solving | Sat Apr 22, 2006 9:15 am

chix475ntu: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon Apr 17, 2006 10:59 am; Thanked: 2 times

by chix475ntu » Sat Apr 22, 2006 9:38 am

between 1 & 2 std below will be 21 - 6 and 21 - 12
ie., between 15 and 9

D

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searchdev: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri Jun 09, 2006 1:02 pm

A little explanation of this question type.

by searchdev » Wed Jun 21, 2006 4:55 am

This question works on normal distribution. Our mean is 21 with a 6 hour standard deviation. So we start to build a chart. 21 in the middle and then start going up by 6 and down by 6. Should look like this:

3 9 15 21 27 33 39

So, the question states that Pat watched 1 and 2 devations BELOW the mean. 15 is 1 deviation below and 9 is 2 deviations below.

The trap here is that they say 1 and two, so we can think of it as between 1 and 2, which is the middle point between 9 and 15, so 12.

I hope this helps. I was very confused when I read this too, but really when it is broken down it is easy. No math, no fomula, no problem.

John

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naveen1003: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Jun 09, 2011 12:54 am; Location: India

by naveen1003 » Thu Jun 09, 2011 1:11 am

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 ?

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

Mean = 21 hours
Standard Deviation = 6 hours
Pat watched television between (mean - 2*standard deviation) and (mean - 1*standard deviation)
between (21- 2*6) and (21 - 1*6)
between 9 and 15
Thus only possible time among all the options is 12
IMO D

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