CAIE S2 2019 November — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2019
SessionNovember
TopicApproximating the Binomial to the Poisson distribution
TypeState Poisson approximation with justification

1 On average, 1 in 150 components made by a certain machine are faulty. The random variable \(X\) denotes the number of faulty components in a random sample of 500 components.
  1. Describe fully the distribution of \(X\).
  2. State a suitable approximating distribution for \(X\), giving a justification for your choice.
  3. Use your approximating distribution to find the probability that the sample will include at least 3 faulty components.