In New York 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 tot the 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 one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was a s shown below and stored in Insurance
73 19 16 64 28 28 31 90 60 56 31 56 22 18
45 48 17 17 17 91 92 63 50 51 69 16 17
a) Construct a 95% confidence interval estimate for the population mean processing time.
b) What assumption must you make about the population distribution order to construct the confidence interval estimate in (a)?
c) Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.