Note: Do all questions. Show your work. Just writing only answers is worth no points. Write dimensions or units with numbers, like hours, ships/day, etc. 1. BBA Bank (a fictitious one) has a drive-through teller window and observed that 15 customers arrive for service per hour, on an average, and the average service time per customer is 3 minutes. Assume inter-arrival time and service time follow a negative Exponential distribution. The bank hires you as a consultant. You guess that this is an MM1 system and you are required to determine the following: a. Probability (teller is busy) ( 3 ) b. Probability (teller is idle) (3) c. Probability of 3 customers in the system. (4) d. Average number of customers waiting for service, that is, number of autos in the line excluding the one at the teller window. (5) e. Average number of customers in the system, that is, number of autos in the line including the one at the teller window. (5) f. Average time a customer spends in the system, that is, waiting time plus service time. (5) g. Average time a customer spends in the waiting line before reaching the teller window