CAIE S1 2021 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2021
SessionJune
TopicApproximating Binomial to Normal Distribution
TypeCombined binomial and normal events

5 Every day Richard takes a flight between Astan and Bejin. On any day, the probability that the flight arrives early is 0.15 , the probability that it arrives on time is 0.55 and the probability that it arrives late is 0.3 .
  1. Find the probability that on each of 3 randomly chosen days, Richard's flight does not arrive late.
  2. Find the probability that for 9 randomly chosen days, Richard's flight arrives early at least 3 times.
  3. 60 days are chosen at random. Use an approximation to find the probability that Richard's flight arrives early at least 12 times.