A bank has two teller counters to serve customers. The average number of customers who come to the bank is $30$ customers per hour, with the distribution of arrivals following the Poisson distribution. Each teller has an average service time of $2$ minutes per customer, with the service time distribution following an exponential distribution. Answer the following questions!

a$)$ Average number of customers in the queue.

b$)$ Average customer waiting time in queue before being served.

c$)$ The probability that there are no customers in the queue.

d$)$ The probability that all tellers are serving customers when two new customers arrive at the same time.

e$)$ If the bank decides to add one additional teller counter, what is the average time

customers wait in line before being served? Explain your decision!