OCR S2 2010 January — Question 9

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2010
SessionJanuary
TopicPoisson Distribution
TypeScaled time period probability

9 Buttercups in a meadow are distributed independently of one another and at a constant average incidence of 3 buttercups per square metre.
  1. Find the probability that in 1 square metre there are more than 7 buttercups.
  2. Find the probability that in 4 square metres there are either 13 or 14 buttercups.
  3. Use a suitable approximation to find the probability that there are no more than 69 buttercups in 20 square metres.
  4. (a) Without using an approximation, find an expression for the probability that in \(m\) square metres there are at least 2 buttercups.
    (b) It is given that the probability that there are at least 2 buttercups in \(m\) square metres is 0.9 . Using your answer to part (a), show numerically that \(m\) lies between 1.29 and 1.3.