CAIE S2 2011 November — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2011
SessionNovember
TopicPoisson Distribution
TypeState conditions only

6 Customers arrive at an enquiry desk at a constant average rate of 1 every 5 minutes.
  1. State one condition for the number of customers arriving in a given period to be modelled by a Poisson distribution. Assume now that a Poisson distribution is a suitable model.
  2. Find the probability that exactly 5 customers will arrive during a randomly chosen 30 -minute period.
  3. Find the probability that fewer than 3 customers will arrive during a randomly chosen 12-minute period.
  4. Find an estimate of the probability that fewer than 30 customers will arrive during a randomly chosen 2-hour period.