A fast food restaurant has a drive-in window. It is estimated that cars arrive according to a Poisson distribution at a rate of 2 every 5 minutes. On average, it takes 1.5 minutes to complete an order, but service time actually varies according to an exponential distribution.
Determine the following:
(i) the probability that the facility is idle.
(ii) the expected number of customers waiting but not currently being served.
(iii) the expected waiting time until a customer can place their order at the counter.
(iv) the expected average non-empty queue.