WJEC Further Unit 2 2022 June — Question 3

Exam BoardWJEC
ModuleFurther Unit 2 (Further Unit 2)
Year2022
SessionJune
TopicPoisson Distribution
TypeSum of independent Poisson processes

3. Two basketball players, Steph and Klay, score baskets at random at a rate of \(2 \cdot 1\) and \(1 \cdot 9\) respectively per quarter of a game. Assume that baskets are scored independently, and that Steph and Klay each play all four quarters of the game.
  1. Stating the model that you are using, find the probability that they will score a combined total of exactly 20 baskets in a randomly selected game.
  2. A quarter of a game lasts 12 minutes.
    1. State the distribution of the time between baskets for Steph. Give the mean and standard deviation of this distribution.
    2. Given that Klay scores at the end of the third minute in a quarter of a game, find the probability that Klay doesn't score for the rest of the quarter.
  3. When practising, Klay misses \(4 \%\) of the free throws he takes. One week he takes 530 free throws. Calculate the probability that he misses more than 25 free throws.