CAIE S2 2021 March — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2021
SessionMarch
TopicLinear combinations of normal random variables
TypeDirect comparison of two variables

5 The volumes, in litres, of juice in large and small bottles have the distributions \(\mathrm { N } ( 5.10,0.0102 )\) and \(\mathrm { N } ( 2.51,0.0036 )\) respectively.
  1. Find the probability that the total volume of juice in 3 randomly chosen large bottles and 4 randomly chosen small bottles is less than 25.5 litres.
  2. Find the probability that the volume of juice in a randomly chosen large bottle is at least twice the volume of juice in a randomly chosen small bottle.