Please help solve this problem.
The residents of Town X spends on avg 21 hours watching television with Standard deviation of 6 hours.
# of hrs Pat watched last week was between 1 and 2 standard deviation below the mean. Which of the following could be the # of hours pat wached last week?
a. 25
b. 20
c. 18
d. 12
e. 10
Thanks in advance.
Standard Deviation
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- Stuart@KaplanGMAT
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The question is a LOT simpler than it sounds. You're really being tested on your understanding of the definition of "standard deviation".kshin78 wrote:You're right. It's d. 12.
It looks like you multiplied the std 6 to 1 & 2 and subtracted from 21 to get the range. Can you please explain why you did that?
Standard deviation measures how numbers are spread out (relative to the mean) in a set. A high standard deviation means that numbers are very spread out; a low standard deviation means that numbers are packed tightly together around the mean.
In this question, the standard deviation is 6 and the mean is 21.
So, 1 standard deviation is 21 +/- 6 (in other words, anyone who watches between 15 and 27 hours of TV is within 1 standard deviation of the mean).
2 standard deviations is 21 +/- (2*6), or 21 +/- 12 (in other words, anyone who watches between 9 and 33 hours of TV is within 2 standard deviations of the mean).
We know that Pat is between 1 and 2 SDs below the mean. Therefore, Pat watches somewhere between:
21-12 and 21-6 = 9 and 15 hours of TV a week.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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Actually, I didn't even look at the choices - 10 is also a valid answer.Hunsi wrote:Stuart Why cant the answer be 10? CHoice E
Where is this question from?
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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Yah.. so either the question is wrong, I messed up somewhere or you mistyped the answer choices... hmmm....kshin78 wrote:the question is from GMAT Prep. That's odd that it would have two valid answers....
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