CAIE S2 2020 March — Question 6

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

6 The volumes, in millilitres, of large and small cups of tea are modelled by the distributions \(\mathrm { N } ( 200,30 )\) and \(\mathrm { N } ( 110,20 )\) respectively.
  1. Find the probability that the total volume of a randomly chosen large cup of tea and a randomly chosen small cup of tea is less than 300 ml .
  2. Find the probability that the volume of a randomly chosen large cup of tea is more than twice the volume of a randomly chosen small cup of tea.