CAIE S2 2007 June — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2007
SessionJune
TopicPoisson Distribution
TypeExplain or apply conditions in context

5 It is proposed to model the number of people per hour calling a car breakdown service between the times 0900 and 2100 by a Poisson distribution.
  1. Explain why a Poisson distribution may be appropriate for this situation. People call the car breakdown service at an average rate of 20 per hour, and a Poisson distribution may be assumed to be a suitable model.
  2. Find the probability that exactly 8 people call in any half hour.
  3. By using a suitable approximation, find the probability that exactly 250 people call in the 12 hours between 0900 and 2100.