1. 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, LQ(t,r) ). You made 5 replications and each replication beginning in the empty and idle state. Simulation run length on each replication is T0+TE=10 hours. Average queue length of each batch in each replication is given in the table below. 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, LQ, 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.)