2. (20 points) Stainless steels can be susceptible to stress corrosion cracking under certain conditions. A materials engineers is interested in determining the proportion of steel alloy failures that are due to stress corrosion cracking. (a) In the absence of preliminary data, how large a sample must be taken so as to be sure that a 98% confidence interval will specify the proportion to within ±0.05? (b) In a sample of 200 failures, 30 of them were caused by stress corrosion cracking. Find a 98% confidence interval for the proportion of failures caused by stress corrosion cracking. (c) Based on the data in part (b), estimate the sample size needed so that the 98% confidence interval will specify the proportion to within ±0.05.