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MATH: How do I solve this standard deviation problem?

T

TommyVercetti

Diamond Member
Not homework, a practice problem out of GMAT.

Brett discovers that 150 bags of his favorite cookie contain a total of 3750 cookies. He then determines that the cookies in a bag are normally distributed with a standard deviation of 5. When Brett goes to the store to buy a bag of his favorite cookies, how many of the 1200 bags in the store contain more than 30 cookies?


24

25

50

192

600



 
I'd say 600, but I didn't think much. I just assume that all bags vary ~5 cookies in either direction, so 50% would have >30 cookies.
 
We know that in a normal distribution (i.e. a bell curve) that 68% of the sample is included in one standard deviation away from the mean, and that 95% is included in two standard deviations.

3750/150 = 25 cookies per bag on average

30 is one standard deviation away from the mean, so that 16% of bags have more than 30 cookies. We know this because 68% of the bags have between 20 - 30 cookies, meaning that 32% are outside this range. Divide that in half to get 16%.

16% of 1200 bags is 192. So Answer D.

I hope that helps, good luck earning your MBA!
 
Pokey is right. Well, pretty much. It's not exactly 68%, that's an estimated rule of thumb, but it works because it fits your answers 🙂
 
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