CAIE S2 2009 June — Question 3

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2009
SessionJune
TopicPoisson Distribution
TypeMultiple independent time periods

3 Major avalanches can be regarded as randomly occurring events. They occur at a uniform average rate of 8 per year.
  1. Find the probability that more than 3 major avalanches occur in a 3-month period.
  2. Find the probability that any two separate 4 -month periods have a total of 7 major avalanches.
  3. Find the probability that a total of fewer than 137 major avalanches occur in a 20 -year period.