A mini supermarket has a cashier who serves $48$ customers per hour on

average during the rushhour. The customers arrive at the rate of $40$

customers per hour. Assuming a single channel queuing model, determine:

a$)$ The probability the cashier is idle

b$)$ The average no$.$ of customers in the queuing system

c$)$ The average time a customer spends in the system

d$)$ The average no$.$ of customers in the queue

e$)$ The average time a customer spends in the queue waiting for the

service