CAIE S2 2012 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2012
SessionJune
TopicPoisson Distribution
TypeScaled time period sums

4 Bacteria of a certain type are randomly distributed in the water in two ponds, \(A\) and \(B\). The average numbers of bacteria per \(\mathrm { cm } ^ { 3 }\) in \(A\) and \(B\) are 0.32 and 0.45 respectively.
  1. Samples of \(8 \mathrm {~cm} ^ { 3 }\) of water from \(A\) and \(12 \mathrm {~cm} ^ { 3 }\) of water from \(B\) are taken at random. Find the probability that the total number of bacteria in these samples is at least 3 .
  2. Find the probability that in a random sample of \(155 \mathrm {~cm} ^ { 3 }\) of water from \(A\), the number of bacteria is less than 35 .