CAIE S2 2014 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2014
SessionJune
TopicApproximating the Binomial to the Poisson distribution
TypeState Poisson approximation with justification

4 The proportion of people who have a particular gene, on average, is 1 in 1000. A random sample of 3500 people in a certain country is chosen and the number of people, \(X\), having the gene is found.
  1. State the distribution of \(X\) and state also an appropriate approximating distribution. Give the values of any parameters in each case. Justify your choice of the approximating distribution.
  2. Use the approximating distribution to find \(\mathrm { P } ( X \leqslant 3 )\).