The arrival of school buses at a maintenance station can be modeled as a Poisson process with a rate of 5 arrivals per day.

(a) What is the probability that exactly 3 buses arrive in a 1-day period?

(b) What is the probability that at least 2 buses arrive in a 1-day period?

(c) What is the probability that at least 3 buses arrive in a 1-day period?

(d) The maintenance station has a policy of requiring buses to wait if the number of buses in maintenance exceeds 6. What is the probability of a bus that must wait for service?

(e) Recompute and plot the occurrence probability of the waiting event in part

(d) as a function of the rate of the Poisson process for rates ranging from 5 to 15.