CAIE S2 2023 June — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2023
SessionJune
TopicPoisson Distribution
TypeMean-variance comparison for Poisson validation

6 It is known that 1 in 5000 people in Atalia have a certain condition. A random sample of 12500 people from Atalia is chosen for a medical trial. The number having the condition is denoted by \(X\).
  1. Use an appropriate approximating distribution to find \(\mathrm { P } ( X \leqslant 3 )\).
  2. Find the values of \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\), and explain how your answers suggest that the approximating distribution used in (a) is likely to be appropriate.