OEI is satisfied that one service technician can handle the $10$ existing customers. Use a waiting line model to determine the following information: $($a$)$ probability that no customers are in the system, $($b$)$ average number of customers in the waiting line, $($c$)$ average number of customers in the system, $($d$)$ average time a customer waits until the service technician arrives, $($e$)$ average time a customer waits until the machine is back in operation, $($f$)$ probability that a customer will have to wait more than one hour for the service technician to arrive, and $($g$)$ the total cost per hour for the service operation.