CAIE S2 2010 June — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2010
SessionJune
TopicApproximating the Binomial to the Poisson distribution
TypeCombined independent Poisson probabilities

6 In restaurant \(A\) an average of 2.2\% of tablecloths are stained and, independently, in restaurant \(B\) an average of 5.8\% of tablecloths are stained.
  1. Random samples of 55 tablecloths are taken from each restaurant. Use a suitable Poisson approximation to find the probability that a total of more than 2 tablecloths are stained.
  2. Random samples of \(n\) tablecloths are taken from each restaurant. The probability that at least one tablecloth is stained is greater than 0.99 . Find the least possible value of \(n\).