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browe235
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Joined: Sat Jan 12, 2013 8:23 am
 

Word Problems Strategy Guide, Medium Practice Questions #14

by browe235 Sun Feb 03, 2013 1:57 pm

This is a quantitative comparison question. Set X consists of 100 bags of rice with an average weight of 90 pounds per bag, and the standard deviation of the weights is 8 pounds.

A = 42
B = the range of weights of the bags of rice in set X.

The correct answer is D, because the range could be bigger, smaller, or equal to 42. However, I have a question about a modified version of this question. Suppose that the question stipulated that this is a normal distribution (I'm assuming it's not). In that case, mustn't it be true that roughly 0.2% of the sample values are necessarily greater than 3 SD's from the mean? And if that is true, then it would follow that whatever the range of the set is, it must be greater than the difference between +3SD and -3SD; 114 (+3 SD) MINUS 66 (-3SD) = 48. Hence, if the distribution were normal, would the answer be B?

Thanks in advance.
tommywallach
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Re: Word Problems Strategy Guide, Medium Practice Questions #14

by tommywallach Sun Feb 10, 2013 10:09 pm

Hey Browe,

You're absolutely right. If this were a normal distribution, we would know a lot about the range. A real question might look like this:

Set X consists of 100 bags of rice with an average weight of 90 pounds per bag. If the weights in the bags are normally distributed, and the standard deviation of the weights is 10 pounds.

A = 40
B = the range of weights of the bags of rice in set X.

This is more the style of the GRE (friendlier numbers!). In this case, because you know that the normal distribution will force some values beyond 2 standard deviations, the full range must be more than 40.

Great question!

-t