A shuttle bus waits at the airport until it is loaded with passengers. Passengers arrive singly according to a Poisson process with rate λ = 20 passengers per hour. The bus is full when eight passengers have arrived.

a. LetT be the time the driver has to wait for the first passenger to arrive, in hours. What is the distribution of T?

b. State E(T), the expected time waited for the first passenger to arrive, in hours.

c. What is the probability the driver has to wait more than 5 minutes for the first passenger to arrive?

d. Find the expected time before eight passengers have arrived and the bus can leave.