In NY State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent to bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of none month, a random sample of 27 approved policies was selected, and the total processing time, in days, was as shown below:
73 19 16 64 28 31
90 60 56 31 56 22
18 45 48 17 17 17
91 92 63 50 51 69
16 17 28
a. Construct a 95% confidence interval estimate for the population mean processing time.
b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?