Need to solve every question step wise with correct answers

SmithTelecome is a supplier to many brand-name makers of mobile phones. SmithTelecome manufactures the external shells that enclose mobile phones. The strength of a shell is measured by applying increasing pressure to the shell and recording the pressure at which the shell breaks. A random sample of 50 shells made by SmithTelecome showed an average strength of 30.0 pounds and a (sample) standard deviation of 5.0 pounds. By hand calculations, construct a 90% confidence interval for the mean shell strength. a. (2 points) Between t and z multiples, which multiple should be used? Explain your answer. Provide the value of the appropriate t or z multiple with the Excel or R formula. Show your work to receive full credit. b. (4 points) State the confidence interval in the two forms: point estimate + margin of error and [lower limit, upper limit]. Show your work to receive full credit. c. (2 points) Interpret the confidence interval within the context of the problem. d. (4 points) What sample size is needed to have 90% confidence of estimating the population mean shell strength to within + 0.5