In New York State, saving accounts are authorized to sell a kind of life insurance called Savings Bank Life insurance (SBLI). The approbation process is integrated by the following steps: checking the application, verifying all medical records by a special agency, petition of additional information if it is necessary. Also is included the compilation of the insurance data to be send to the bank for further processing. During one month, it has been selected a simple random sample of 27 approved insurances with their respective processing time (in days). The results are the following: 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. In the past the mean processing time was 45 days. At the 0.05 level of significance is there evidence that the mean processing time has changed from 45 days?
b. What assumption about the population distribution is needed in order to conduct the t-test in (a)
c. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b)
d. Do you think that the assumption needed in order to conduct the t test in (a) is valid? Explain