CAIE S2 2005 November — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2005
SessionNovember
TopicPoisson Distribution
TypeFinding minimum stock level for demand

6 A shopkeeper sells electric fans. The demand for fans follows a Poisson distribution with mean 3.2 per week.
  1. Find the probability that the demand is exactly 2 fans in any one week.
  2. The shopkeeper has 4 fans in his shop at the beginning of a week. Find the probability that this will not be enough to satisfy the demand for fans in that week.
  3. Given instead that he has \(n\) fans in his shop at the beginning of a week, find, by trial and error, the least value of \(n\) for which the probability of his not being able to satisfy the demand for fans in that week is less than 0.05 .