CAIE S2 2018 June — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2018
SessionJune
TopicPoisson Distribution
TypeExplain or apply conditions in context

6 Accidents on a particular road occur at a constant average rate of 1 every 4.8 weeks.
  1. State, in context, one condition for the number of accidents 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 4 accidents will occur during a randomly chosen 12-week period.
  3. Find the probability that more than 3 accidents will occur during a randomly chosen 10 -week period.
  4. Use a suitable approximating distribution to find the probability that fewer than 30 accidents will occur during a randomly chosen 2 -year period ( \(104 \frac { 2 } { 7 }\) weeks).