CAIE S2 2022 June — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionJune
TopicPoisson Distribution
TypeSum of independent Poisson processes

5 Cars arrive at a fuel station at random and at a constant average rate of 13.5 per hour.
  1. Find the probability that more than 4 cars arrive during a 20-minute period.
  2. Use an approximating distribution to find the probability that the number of cars that arrive during a 12-hour period is between 150 and 160 inclusive.
    Independently of cars, trucks arrive at the fuel station at random and at a constant average rate of 3.6 per 15-minute period.
  3. Find the probability that the total number of cars and trucks arriving at the fuel station during a 10 -minute period is more than 3 and less than 7 .