An apartment complex is considering hiring a security guard for its parking lot. Based upon information obtained from similar apartment complexes, it is believed that cars will arrive at the parking lot at the rate of $27\mathrm{.}5$ per hour. It takes an average of two minutes for the security guard. to process a car. Assuming that the system to be an $\frac{M}{M}\frac{?}{1}$ queueing system, find:

$($a$)$ the proportion of the time that the security guard is busy.

$($b$)$ the average number of cars waiting in line to enter the parking lot.

$($c$)$ the expected time a car spends just waiting in line to enter the parking lot.