A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon to 1 pm lunch period. The waiting time (defined as the time from when customers join the queue until they reach the teller’s window) of all customers during this hour is recorded over a period of one week. A random sample of 15 customers is selected, and the results are as follows: < bank1="">

4.21     5.55     3.02     5.13     4.77     2.34     3.54     3.20

4.50     6.10     0.38     5.12     6.46     6.19     3.79

a. At the 0.05 level of significance, is there sufficient evidence that the mean waiting time is less than 5 minutes?

b. What assumption must hold in order to perform the test in (a)?

c. Evaluate this assumption through a graphical approach. Discuss.

d. As a customer walks into the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, ‘Almost certainly not longer than 5 minutes’. On the basis of the results of (a), evaluate this statement