CAIE S2 2014 November — Question 2

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

2 The probability that a randomly chosen plant of a certain kind has a particular defect is 0.01 . A random sample of 150 plants is taken.
  1. Use an appropriate approximating distribution to find the probability that at least 1 plant has the defect. Justify your approximating distribution. The probability that a randomly chosen plant of another kind has the defect is 0.02 . A random sample of 100 of these plants is taken.
  2. Use an appropriate approximating distribution to find the probability that the total number of plants with the defect in the two samples together is more than 3 and less than 7 .