1.Trash Bags.Buckeye Trash Solutions (BTS) feels that their new, improved 30 gallon trash bag will be the strongest bag on the market if the new trash bag's mean breaking strength can be shown to be at least 50 pounds.This means that the garbage bag will hold at least 50 pounds.A random sample of 75 new, improved trash bags reveals lbs.Assume .

a)Define _____________________________________________________________________.

b)Calculate 95% and 99% confidence intervals for .

c)Can BTS be 95% confident that is at least 50 lbs? Explain.

d)Can BTS be 99% confident that is at least 50 lbs? Explain.

e)Based on your answer to c)and d), how convinced are you that the new 30 gallon trash bag is the strongest such bag on the market?

f)Estimate the sample size needed so that a 97% confidence interval would be (50, 51.15).Show all work.