Consider you model a call center that serve 7/24 and your concern is reducing the waiting times of customers in the call queue (Your response variable is queue length, Lo(t,r)). You made 5 replications and each replication beginning in the empty and idle state. Simulation run length on each replication is To+TE= 10 hours. Average queue length of each batch in each replication is given in the table below. Batch 1 2 3 4 67495 8 10 Replication r 2 1 11.20 15.30 18.56 14.87 17.98 17.30 14.11 17.52 13.86 14.98 12.30 11.40 18.28 19.36 13.66 13.25 12.40 15.92 4 17.08 18.00 3 10.80 10.09 10.38 12.51 15.57 11.65 12.05 16.70 18.91 15.00 4 10.50 10.42 19.82 17.50 15.20 11.12 14.29 13.79 15.89 15.78 5 11.70 11.84 16.89 18.26 14.82 19.50 19.40 10.07 15.23 19.25 a. Show that there is an initialization bias, and this bias can be reduced by deletion of one or more observations. (Please compute no deleted, d=1 and d=2). b. Construct a 95% confidence interval on the long-run average queue length for no delete, d=1 and d 2. Please explain why the confidence interval widens as the batches are deleted. c. How many replications are needed to estimate the long-run mean queue length, Lo, if it is important to detect a difference of 3 customers with 90% confidence interval (when d-2). (You can use Excel if calculations are long and can write your answers. However, please write equations you used.)