Edexcel S2 2018 January — Question 5

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2018
SessionJanuary
TopicPoisson Distribution
TypeConsecutive non-overlapping periods

5. A delivery company loses packages randomly at a mean rate of 10 per month. The probability that the delivery company loses more than 12 packages in a randomly selected month is \(p\)
  1. Find the value of \(p\) The probability that the delivery company loses more than \(k\) packages in a randomly selected month is at least \(2 p\)
  2. Find the largest possible value of \(k\) In a randomly selected month,
  3. find the probability that exactly 4 packages were lost in each half of the month. In a randomly selected two-month period, 21 packages were lost.
  4. Find the probability that at least 10 packages were lost in each of these two months.
  5. Using a suitable approximation, find the probability that more than 27 packages are lost during a randomly selected 4-month period.