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Problem 15 Easy Difficulty

The 'Garbage Project" at the University of Arizona reports that the amount of paper discarded by households per week is normally distributed with mean 9.4 lb and standard deviation 4.2 lb. What percentage of households throw out at least 10 lb of paper a week?

Answer

44.3$\%$ of the Households throw more than 10 lbs of paper a week

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Video Transcript

Okay, So for this part of the problem, um, you've given some useful information. So it is reported that this the function there's modeling. This particular problem is normal things to it. So you have. No, I mean, you can You can You can write off of t as one over on your signal it and it is quite a troop. I time you explained your year to the miners have any of X minus mu. And then this is true for all x ray than any courses you and F will be zero for all extensions. You. So that's what I think is actually not t intend to you. Thanks you. So Leary's this So after vaccines defined that way, So make notice correct in years of X equals that and, uh, some of the useful information we're even is that mule. So you either mean so meal is 9.4. So £9.4 and then you are sigma would use the standard deviation just £4.2. So before you jump into solvable problem, it's always good to have you Can you give me and try to makes sense of each one of them toe. Ask yourself if you understand what each one off the variable means for the first requirement that f us to be normal. It is too muted. I would just like to find here, um and then you get into clamorous, so you give it new. We just mean is four is 9.4 and then Sigmund the standing ovations for two. Now, if you have this information is very easy to after the question. So we will let you know, uh, the percentage of household that throw at least thrown at least £10 paper a week. So this is this'll problem issue into asking what is P. L T is greater than right. Anything close 10 £10. Now, if you translated, it isn't an integral becomes into go from 10 to infinity. Now, then you have of X t x. So when you plug this into you, I'm gonna take out Constance. I'm not gonna worry about actual integral, so I'll get one of Sigma. Well, I could I'm gonna start using the values. So So instead of using Sigma, I know what said my sigma is it is four foreign to pound and then this is multiplying square or to buy. And then now the inter goes going from 10 to infinity and you need to the minus 1/2 X minus new. So near the mean is 9.4. So you can put that in there and then you have a Sigma Sigma is 4.2. These old things squared DX. So I'm in trouble like this has not. It doesn't have a savage forms. You can look this up so an integral like this, you can use maple. Or you can use Wolfram. We just available free on the Web yet, Wolfram. So for my kid, I'm gonna use maypole. So if I use Maple Um, yeah, so, like, I basically just fine And your medical calculator, Um I mean, an integral California that's gonna help you as you value disintegrate. So if you you you do maypole, uh, you should end up with, you know, you know, for for or 44%. So this is this is this is Thea. This is the answer we're looking for right here.