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Standard Deviation

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by veenu08 » Sun Oct 06, 2013 6:36 am
The fourth grade at school X is made up of 300 students who have a total weight of 21,600 pounds. If the weight of these fourth graders has a normal distribution and the standard deviation equals 12 pounds, approximately how many of these fourth graders weigh more than 84 pounds?

1. 12
2. 16
3. 36
4. 48
5. 60
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by Brent@GMATPrepNow » Sun Oct 06, 2013 6:52 am
This question is out of scope; normal distributions are not tested on the GMAT.

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by theCodeToGMAT » Sun Oct 06, 2013 7:01 am
Students 300

Weight 21600

Mean = 72

First SD = 72+12 = 84
The percentage corresponding to 84+ --> 13.5 + 2.5 approx = 16%

So, 16% of 300 = 48

Answer [spoiler]{D}[/spoiler]
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by ani781 » Mon Oct 07, 2013 5:06 am
RAHUL, how did you arrive at the 16 ? Can you pls clarify.
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by theCodeToGMAT » Mon Oct 07, 2013 5:31 am
ani781 wrote:RAHUL, how did you arrive at the 16 ? Can you pls clarify.
I will draw to explain..

Image


The percentageS marked in this diagram are FIXED.

S.D. is basically a deviation from MEAN.. and FIRST, SECOND & THIRD Deviation tells the distribution of people at each SD Interval.
For example: First SD from MEAN = 34%(Scores above Mean) + 34%(Scores below Mean)

Now, the questions asks us to find students above 84(that means right side of the graph).. we know SD = 12.. we found mean as 72
First SD = 72 + 12 = 84
All the students after First S.D. will have weight above 84...
So, (50 - 34 ) = 16%

Is it fine now?
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