Question: Automobiles arrive at a tollbooth on a highway completely at random according to a Poisson process with rate λ = 4 cars per hour. Determine the following:
a. The probability that the time between any two successive arrivals exceeds 20 minutes.
b. The probability that exactly four cars arrive in any given hour.
c. The probability that more than five cars arrive in any given hour.
d. The probability that more than 10 cars arrive in any given two-hour period.
e. A person working for the transportation department begins counting arrivals at the tollbooth at 8 A.M. What is the probability that he counts 20 arrivals before 12 noon? (Use a normal approximation for your calculations.)