Question

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 to 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 as shown below and stored in the file 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 and interpret a 95% confidence interval estimate of the population mean processing time. Use Minitab. (Don't worry about this one.)

b. What assumption must you make about the population distribution in order to construct the confidence interval in (a)?

c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

Answer 1

Part a

Required 95% confidence interval by using Minitab is given as below:

Variable          N      Mean     StDev   SE Mean

Time             27     43.89     25.28      4.87

Variable             95.0% CI           

Time          (   33.89,   53.89)    

Confidence interval = (33.89, 53.89)

Part b

The assumption of normality we must make about the population distribution in order to construct the above confidence interval.

Part c

Yes, assumption needed in order to construct the confidence interval is valid because the variable total processing time is approximately normally distributed.