A recycling plant compresses aluminum cans into bales. Theweights of the resulti

Question

A recycling plant compresses aluminum cans into bales. Theweights of the resulting bales are known to follow a distributionwith standard deviation = 12.5 pounds(lbs). Averages of several measurements are less variable thanindividual measurements. Assume that the weights of the balesfollow a normal distribution. In this case, the mean of15 randomly selected bales also has anormal distribution. a) What is the probability that the weight of a randomly selectedbale is more than 6 lb. above or belowthe population mean?
b) What is the probability that the mean weight of15 randomly selected bales is morethan 6 lb. above or below thepopulation mean? To start this question off, I calculated the standarddeviation of the mean of an SRS of 15 bales to be 3.23 but aftercalculating that I have no idea what to do next. Any help would begreatly appriciated! A recycling plant compresses aluminum cans into bales. Theweights of the resulting bales are known to follow a distributionwith standard deviation = 12.5 pounds(lbs). Averages of several measurements are less variable thanindividual measurements. Assume that the weights of the balesfollow a normal distribution. In this case, the mean of15 randomly selected bales also has anormal distribution. b) What is the probability that the mean weight of15 randomly selected bales is morethan 6 lb. above or below thepopulation mean? To start this question off, I calculated the standarddeviation of the mean of an SRS of 15 bales to be 3.23 but aftercalculating that I have no idea what to do next. Any help would begreatly appriciated!

Explanation / Answer

X=weight of bales with mean and =12.5 and inormally distributed Xbar is ased on a sample of 15 bales and is normal with mean andxbar=/n=12.5/15=3.23 a)P(-6>X>+6)=2P(X<-6) by symmetryof the normal..................................(1) Using the standard Normal we have Z=(X-)/ or X=+Z. Substituting into (1) 2P(+Z<-6)=2P(Z<-6/)=2P(Z<-.48)=2(.316)=.632 (b)In this case the rv is Xbar andXbar=/15=3.23 Using same approach as above now with Z=(Xbar-)/3.23 Hence 2P(Xbar<-6)=2P(Z<-6/3.23)=2P(Z<-1.86)=.0314

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.