CAIE S2 2017 March — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2017
SessionMarch
TopicLinear combinations of normal random variables
TypeComparison involving sums or multiples

6 The masses, in kilograms, of cartons of sugar and cartons of flour have the distributions \(\mathrm { N } \left( 78.8,12.6 ^ { 2 } \right)\) and \(\mathrm { N } \left( 62.0,10.0 ^ { 2 } \right)\) respectively.
  1. The standard load for a certain crane is 8 cartons of sugar and 3 cartons of flour. The maximum load that can be carried safely by the crane is 900 kg . Stating a necessary assumption, find the percentage of standard loads that will exceed the maximum safe load.
  2. Find the probability that a randomly chosen carton of sugar has a smaller mass than a randomly chosen carton of flour.