The new accounts loan officer of the Citizens Northern Savings Bank interviews all customers for new accounts. The customers desiring to open new accounts arrive at the rate of $4$ per hour, according to a Poisson distribution, and the accounts officer spends an average of $12$ minutes with each customer, setting up a new account. $($show all your work to receive full credits, $10$ points$)$ Q$1$: Probability of no customers in the system Q$2$: How many customers are in the queuing system on average? Q$3$: How many customers are in the waiting line on average? Q$4$: What is the average time in the system per customer. Q$5$: What is the average time in the waiting line Q$6$: Probability that the new account officer is busy, and a customer must wait.