Edexcel S2 2022 January — Question 5

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2022
SessionJanuary
TopicApproximating the Binomial to the Poisson distribution
TypeState exact binomial distribution

5 Applicants for a pilot training programme with a passenger airline are screened for colour blindness. Past records show that the proportion of applicants identified as colour blind is 0.045
  1. Write down a suitable model for the distribution of the number of applicants identified as colour blind from a total of \(n\) applicants.
  2. State one assumption necessary for this distribution to be a suitable model of this situation.
  3. Using a suitable approximation, find the probability that exactly 5 out of 120 applicants are identified as colour blind.
  4. Explain why the approximation that you used in part (c) is appropriate. Jaymini claims that 75\% of all applicants for this training programme go on to become pilots. From a random sample of 96 applicants for this training programme 67 go on to become pilots.
  5. Using a suitable approximation, test Jaymini's claim at the \(5 \%\) level of significance. State your hypotheses clearly.