CAIE S2 2021 June — Question 7

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2021
SessionJune
TopicLinear combinations of normal random variables
TypeMixed sum threshold probability

7 The masses, in kilograms, of large and small sacks of flour have the distributions \(\mathrm { N } \left( 55,3 ^ { 2 } \right)\) and \(\mathrm { N } \left( 27,2.5 ^ { 2 } \right)\) respectively.
  1. Some sacks are loaded onto a boat. The maximum load of flour that the boat can carry safely is 340 kg . Find the probability that the boat can carry safely 3 randomly chosen large sacks of flour and 6 randomly chosen small sacks of flour.
  2. Find the probability that the mass of a randomly chosen large sack of flour is greater than the total mass of two randomly chosen small sacks of flour.