dolution

A university cafeteria is a self-service facility in which a customer selects the food items he/she wants and pays the cashier following a single line. Customers arrive on average every after 2.5 minute that approximately follows the Poisson distribution. The single cashier ringing up sales takes about 2 minutes per customer, following the negative exponential distribution. i. What is the utilization rate of serving the customer? ii. What is the average number of customers in the system? iii. What is the average number of customers in the waiting line? iv. What is the probability of more than 6 customers in the system? v. What is the probability of spending more than 10 minutes in the system?