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. A random sample of 50 new, improved trash bags reveals . = 50.75 Ibs. Assume o = 2.65. a) Define Hi b) Calculate 95% and 99% confidence intervals for u. c) Can BTS be 95% confident that a is 50 Ibs? Explain d) Can BTS be 99% confident that a is 50 lbs? Explain. ) 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 96% confidence interval would be (50, 51.15). Show all work.2. Debt-to-Equity Ratio. One measure of a company's financial health is its debt-to-equity ratio. This quantity is defined to be the ratio of the company's corporate debt to the company's equity. If this ratio is too high, it is one indication of financial instability. For obvious reasons, banks often monitor the financial health of companies to which they have extended commercial loans. Suppose that, in order to reduce risk, Loans-R-Us has decided to initiate a policy limiting mean debt-to-equity ratio for its portfolio of commercial loans to being less than 1.5. In order to estimate the mean debt-to-equity ratio of its current commercial loan portfolio, the bank randomly selects a sample of 15 of its commercial loan accounts. Audits of these 15 companies sampled result in the following debt-to-loan ratios: 1.31 1.05 1.45 1.21 1.29 1.78 1.37 1.41 1.22 1.11 1.46 1.23 1.29 1.32 1.65 a. What is the parameter Loans-R-Us wishes to estimate? b. Find a 95% confidence interval. c. Interpret this confidence interval in the context of the problem. d. Based on the interval, is Loans-R-Us in compliance with its new policy