Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate per hour. Suppose that with probability .5 an arriving vehicle will have no equipment violations.

a 5 10 1 sq mile 5 640 acres X 5 the number E(X) 5 m

a. What is the probability that exactly ten arrive during the hour and all ten have no violations?

b. For any fixed , what is the probability that y arrive during the hour, of which ten have no violations?

c. What is the probability that ten “no-violation” cars arrive during the next hour? [Hint: Sum the probabilities in part

(b) from to .]