CAIE S2 2020 June — Question 3

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionJune
TopicLinear combinations of normal random variables
TypeDirect comparison of two variables

3 The masses, in kilograms, of large sacks of flour and small sacks of flour have the independent distributions \(\mathrm { N } \left( 40,1.5 ^ { 2 } \right)\) and \(\mathrm { N } \left( 12,0.7 ^ { 2 } \right)\) respectively.
  1. Find the probability that the total mass of 6 randomly chosen large sacks of flour is more than 245 kg .
  2. Find the probability that the mass of a randomly chosen large sack of flour is less than 4 times the mass of a randomly chosen small sack of flour.