Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially, with mean 3 minutes. Find:

(i) the probability that an arrival finds that four persons are waiting for their turn;

(ii) the average number of persons waiting and making telephone calls; and

(iii) the average length of the queue that is formed from time to time.