Tourists arrive at a historic park (for simplicity, one at a time) according to a Poisson process at a rate of 40 per hour. Each five people take an excursion in a minivan. Let N_t be the number of excursions arranged by time t.

(a) Show that N_t is a renewal process. What is the distribution of the time between consecutive “renewals” (excursions)? Find the probability that an interarrival time will exceed 10 minutes.

(b) What is the number of excursions per hour in the long run?

(c) Estimate the probability that the number of excursions during eight working hours will fall into the interval [60,70].