CAIE S2 2014 June — Question 7

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2014
SessionJune
TopicPoisson Distribution
TypeState conditions only

7 A Lost Property office is open 7 days a week. It may be assumed that items are handed in to the office randomly, singly and independently.
  1. State another condition for the number of items handed in to have a Poisson distribution. It is now given that the number of items handed in per week has the distribution \(\operatorname { Po } ( 4.0 )\).
  2. Find the probability that exactly 2 items are handed in on a particular day.
  3. Find the probability that at least 4 items are handed in during a 10-day period.
  4. Find the probability that, during a certain week, 5 items are handed in altogether, but no items are handed in on the first day of the week.