Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new , improved trash bag feel sure that it's 30 gallon bag will be the strongest such bag on the market if the new trash bag's mean breaking strengths can be shown to be a least 50 pounds. The mean of the sample of 40 trash bag breakiing strengths 1.9 is x = 50.575. If we let m denote the mean of the breaking strengths of all possible trash bags of the new type and assume the "O" the standard deviation equals 1.65.

a. Calculate 95% and 99% confidence intervals for m.

b. Using the 95% confidence intervals, can we be 95% confident that m is a least 50 pounds? Explain.

c. Using the 99% confident interval, can we be 99% confident that m is at least 50 pounds? explain.
Based on your answer to parts b and c, how convinced are you that the new 30- gallon trash bag is the strongest such bag on the market.