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Standard Deviation

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by gvosough » Tue Feb 22, 2011 12:29 am
thirty children acquired a total of 2700 baseball cards. if 16% had fewer than 70 baseball cards and the number of cards per child has a normal dist, what percent of the children had greater than 130 baseball cards?
A)2
B)4
C)14
D)34
E)68

OA: A
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by Target2009 » Sat Feb 26, 2011 10:09 am
IMO : A
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by Stuart@KaplanGMAT » Sat Feb 26, 2011 11:47 am
gvosough wrote:thirty children acquired a total of 2700 baseball cards. if 16% had fewer than 70 baseball cards and the number of cards per child has a normal dist, what percent of the children had greater than 130 baseball cards?
A)2
B)4
C)14
D)34
E)68

OA: A
What's the source of this question? I have two serious problems with it.

First, I have never heard of nor seen an actual GMAT question that used the phrase "normal distribution"; to the best of my knowledge, test takers are not expected even to know what a normal distribution is, let alone memorize the percent breakdown for one.

Second, even if you know the values for a normal distribution there's a lot of grunt work on the question (using the 2700/30 to calculate the mean, then using the 16% below 70 to calculate the value of one standard deviation, then using the value of one standard deviation to find out how many SDs 130 is from the mean) - way more than can reasonably be expected on even a 770 level GMAT question.

I supposed that once you calculate the mean (90) and see that 130 is substantially further from the mean than is 70 you can very quickly eliminate C, D and E (even without knowing what the figures are for a normal distribution), but unless someone provides anecdotal evidence of seeing a "normal distribution" question on the actual GMAT, I'm going to stick with "ignore this question entirely, it's beyond the scope of the exam".
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by Night reader » Sat Feb 26, 2011 12:32 pm
Standard deviation is S, mean is w
less than 70 baseball cards is below 90 baseball cards (mean, w); only two children own this much (less than 70 cards) out of 30. Mean (w=90) is 20 more than the 16% or less than 70 and; less than 70 is 40 less less than more than 130.

Assume 16% is within (3S-2S) or 1S range from the mean, we need to find S then. Let's take all baseball cards are spread within 3S below the mean and 3S above the mean, or total 6S range. Then 2,700/6=S or S=450 and out of 450 we have the baseball cards less than 70, which means that we may not have 4% interval range in the beginning of our distribution set, and we need to have 2% (or 98% precision) 450-(>70)=(>)380

I agree with Stuart this problem is not the one for GMAT, rather stats assignment.
gvosough wrote:thirty children acquired a total of 2700 baseball cards. if 16% had fewer than 70 baseball cards and the number of cards per child has a normal dist, what percent of the children had greater than 130 baseball cards?
A)2
B)4
C)14
D)34
E)68

OA: A
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