On a summer day, buses with tourists arrive in the picturesque village of Edam according to Poisson process with average of 5 buses per hour. The village of Edam is world famous for its cheese. Each bus stays either one hour or 2 hours in Edam with equal probabilities.
(a) What is the probability distribution of number of tourist buses in Edam village at 4 o'clock in the afternoon?
(b) Each bus brings 50, 75, or 100 tourists with respective probabilities 1/4, 1/2, and 1/4 respectively. Calculate a normal approximation to the probability that more than 1000 bus tourists are in Edam village at 4:00 o'clock in the afternoon. (Hint: the number of bus tourist is distributed as the convolution of two compound Poisson distributions.)