Consider a waiting line system with the arrival rate being $10$ customers per hour and the service on a customer is $12$ minutes on average. Assume that both inter$-$arrival time and service time follow exponential distribution.

$($a$)$ What$$s the arrival rate and service rate $($customers per hour$)?[5$ pts$]$

$($b$)$ What is the minimum number of servers that are required to ensure the customer$$s average waiting time in queue is no more than $5$ minutes? $[5$ pts$]$

$($c$)$ What is the minimum number of servers that are required to ensure the average number of people in the system is no more than $4?[5$ pts$]$