CAIE S2 2021 November — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2021
SessionNovember
TopicPoisson Distribution
TypeSum of independent Poisson processes

5 In a certain large document, typing errors occur at random and at a constant mean rate of 0.2 per page.
  1. Find the probability that there are fewer than 3 typing errors in 10 randomly chosen pages.
  2. Use an approximating distribution to find the probability that there are more than 50 typing errors in 200 randomly chosen pages.
    In the same document, formatting errors occur at random and at a constant mean rate of 0.3 per page.
  3. Find the probability that the total number of typing and formatting errors in 20 randomly chosen pages is between 8 and 11 inclusive.