The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with an arrival rate of $5$ boats per hour, and that service times follow an exponential prob$-$ ability distribution, with a service rate of $10$ boats per hour. Answer the following questions: a$.$ What is the probability that no boats are in the system?$$b$.$ What is the average number of boats that will be waiting for service? c$.$ What is the average time a boat will spend waiting for service? d$.$ What is the average time a boat will spend at the dock? e$.$ If you were the manager of Fore and Aft Marina, would you be satisfied with the$$service level your system will be providing? Why or why not?