SG #5 Word problems, Chapter 10 Medium question #14

[johnhurford]

Hi,

I'm trying to understand this problem better. The givens for the set are...

mean = 90 lbs/bag
standard deviation (SD) = 8 lbs

Doing calculations to figure out the weight of bag A and weight of bag B....

Bag A = 90 - 2*8 = 74 lbs
Bag B = 90 + 5 = 95 lbs

QA = 2*(95-74) = 42

QB is where I am not understanding this problem. If the mean is 90 and the SD is 8, then plus and minus 3 SD (of 99% of all observations right?) would provide a range of [90 + 3*(8)] - [90 - 3*(8)] = 48. I would suspect that the range of the given set would at least be 48 (since 0.1% of the observations lie outside plus or minus 3 SD of mean). Why is this not (48 or more) the right answer for QB?

[tommywallach]

Hey John,

I think you're assuming this set is normally distributed. But standard deviation CAN exist outside of normal distributions (it's just WAY more complicated--more complicated than the GRE will ever test). In this case, the percentages you're thinking of don't actually hold in the clear way they do for normally distributed sets, so we can't know how much exists where. Hope that helps!

-t