b) A university cafeteria is a self-service facility in which a customer selects the food items...

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b) A university cafeteria is a self-service facility in which a customer selects the food items he/she wants and then following a single line pays the cashier. Customers arrive at a rate of about 5 per minute according to the Poisson distribution. The single cashier ringing up sales takes about 10 seconds per customer, following the negative exponential distribution. i. What is the utilization rate of serving the customer? ii. What is the probability of no customer in the system? i11. iv. <3 V. What is the average number of customers in the system? What is the average number of customers in the line? What is the probability that there are over 6 customers in the system? b) A university cafeteria is a self-service facility in which a customer selects the food items he/she wants and then following a single line pays the cashier. Customers arrive at a rate of about 5 per minute according to the Poisson distribution. The single cashier ringing up sales takes about 10 seconds per customer, following the negative exponential distribution. i. What is the utilization rate of serving the customer? ii. What is the probability of no customer in the system? i11. iv. <3 V. What is the average number of customers in the system? What is the average number of customers in the line? What is the probability that there are over 6 customers in the system?