2 The average numbers of cars, lorries and buses passing a point on a busy road in a period of 30 minutes are 400, 80 and 17 respectively.
- Assuming that the numbers of each type of vehicle passing the point in a period of 30 minutes have independent Poisson distributions, calculate the probability that the total number of vehicles passing the point in a randomly chosen period of 30 minutes is at least 520.
- Buses are known to run in approximate accordance with a fixed timetable.
Explain why this casts doubt on the use of a Poisson distribution to model the number of buses passing the point in a fixed time interval.