The counter of a bank branch performs the transactions with a mean time of $2$ minutes. The customers arrive at a mean rate of $20$ customers$/$hour$.$ If we assume that arrivals follow a Poisson process and that the service time is exponential, determine:

$($a$)$ Percentage of the time the bank teller is idle $($b$)$ Mean waiting time of the customers

$($c$)$ Percentage of customers that wait in a queue