CAIE S2 2019 March — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2019
SessionMarch
TopicPoisson Distribution
TypeFinding minimum n for P(X≥k) threshold

5 The number of eagles seen per hour in a certain location has the distribution \(\operatorname { Po } ( 1.8 )\). The number of vultures seen per hour in the same location has the independent distribution \(\operatorname { Po } ( 2.6 )\).
  1. Find the probability that, in a randomly chosen hour, at least 2 eagles are seen.
  2. Find the probability that, in a randomly chosen half-hour period, the total number of eagles and vultures seen is less than 5 .
    Alex wants to be at least \(99 \%\) certain of seeing at least 1 eagle.
  3. Find the minimum time for which she should watch for eagles.