The arrival of aircraft to an airport can be modeled as a Poisson process with a rate of 10 arrivals per hour.

(a) What is the probability that exactly 5 aircrafts arrive in a 1-h period?

(b) What is the probability that at least 5 aircrafts arrive in a 1-h period?

(c) What is the probability that at least 10 aircrafts arrive in a 1-h period?

(d) The airport has a policy of requiring aircraft to wait in a holding position in the air if the number of arriving aircraft in any 10-min period exceeds 2. What is the occurrence probability of an aircraft holding event?

(e) Recompute and plot the occurrence probability of an aircraft holding event in part

(d) as a function of the rate of the Poisson process for rates ranging from 10 to 50.