Q.2. Consider a bank with five tellers and one queue, which opens its doors at 9 A.M. closes its doors at 5PM., but stays open until all customers in the bank at 5PM. have been served. Assume that customers arrive in accordance with a Poisson process at rate 1 per minute (ie.. IID exponential interarrival times with mean 1 minute), that service times are TID exponential random variable with mean 4 minutes, and that customers are served in a FIFO manner. Table below shows several typical output statistics from 10 independent replications of a simulation of the bank, assuming that no customers are present initially. Note that results from various replications can be quite different. Thus, one run clearly does not produce the answers". a) Obtain a point estimate and approximate 90 percent confidence interval for the expected average delay of a customer over a day. (20-Mark) b) Obtain a point estimate and an approximate 90 percent confidence interval for the expected proportion of customers with a delay less than 5 minutes over a day, which is given by (10-Mark) E(X)= E - 1,(0,5) 1 N 1 (0,5) = (1, 10, if DS5 otherwise For i=1,2..., N. in queue Replication 1 2 3 4 5 Results for 10 independent replications of the bank model Average delay Proportion of Number Finished Time Average queue customers delayed served (hours) minutes) Length