Edexcel S2 2023 January — Question 5

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2023
SessionJanuary
TopicPoisson Distribution
TypePoisson with binomial combination

  1. A company produces steel cable.
Defects in the steel cable produced by this company occur at random, at a constant rate of 1 defect per 16 metres. On one day the company produces a piece of steel cable 80 metres long.
  1. Find the probability that there are at most 5 defects in this piece of steel cable. The company produces a piece of steel cable 80 metres long on each of the next 4 days.
  2. Find the probability that fewer than 2 of these 4 pieces of steel cable contain at most 5 defects. The following week the company produces a piece of steel cable \(x\) metres long.
    Using a normal approximation, the probability that this piece of steel cable has fewer than 26 defects is 0.5398
  3. Find the value of \(x\)