CAIE S2 2022 June — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionJune
TopicPoisson Distribution
TypeSingle period normal approximation

5 The number of clients who arrive at an information desk has a Poisson distribution with mean 2.2 per 5-minute period.
  1. Find the probability that, in a randomly chosen 15 -minute period, exactly 6 clients arrive at the desk.
  2. If more than 4 clients arrive during a 5 -minute period, they cannot all be served. Find the probability that, during a randomly chosen 5 -minute period, not all the clients who arrive at the desk can be served.
  3. Use a suitable approximating distribution to find the probability that, during a randomly chosen 1-hour period, fewer than 20 clients arrive at the desk.