CAIE S2 2023 November — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2023
SessionNovember
TopicApproximating the Poisson to the Normal distribution
TypeMultiple approximations in one question

1
  1. A random variable \(X\) has the distribution \(\operatorname { Po } ( 25 )\).
    Use the normal approximation to the Poisson distribution to find \(\mathrm { P } ( X > 30 )\).
  2. A random variable \(Y\) has the distribution \(\mathrm { B } ( 100 , p )\) where \(p < 0.05\). Use the Poisson approximation to the binomial distribution to write down an expression, in terms of \(p\), for \(\mathrm { P } ( Y < 3 )\).