A self-service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find (i) the average number of customers in the system. (in) the average number of customers in queue or average queue length. (iii) the average time a customer spends on the system. (iv) the average time a customer waits before being served. (v) the probability that a person arriving at the store will have to wait in the queue. (vi) the probability that it will take more the 6 min to wait for service. (vii) the chance that it will take him more than 10 min altogether to wait for service and complete his billing. (viii) the fraction of the day when the cashier will be busy. (ix) the probability that the number in the system exceeds 4 (x) the average length of the queue that forms from time to time. (xi) the average queue length that forms from time to time. (xii) the average waiting time in the queue if he has to wait. The self-service store will appoint a second cashier when convinced that an arrival must wait on average for at least 3 min for service. How much should the flow of arrivals increase to justify a second A