A paint manufacturer is developing a new type of paint. They are interested in finding the mean life of the paint before corrosion occurs. Thirty panels were exposed to various corrosive conditions to measure the protective ability of the paint. The mean life for the samples was 168 hours before corrosive failure. Based on past experience, for a paint of similar type, the life time of paint before corrosion had population standard deviation of 30 hours. (a) Find the 95% confidence interval for the mean life of the paint. Interpret the result. (C) (b) What is the point estimate of the true mean life of the paint. The company decides to market the new paint only when there is evidence of life of 170 hours before corrosive failure. Based on your answer in part-a, what should the company do and why?