CAIE S2 2018 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2018
SessionJune
TopicLinear combinations of normal random variables
TypeDistribution of scaled variable

4 The volume, in millilitres, of a small cup of coffee has the distribution \(\mathrm { N } ( 103.4,10.2 )\). The volume of a large cup of coffee is 1.5 times the volume of a small cup of coffee.
  1. Find the mean and standard deviation of the volume of a large cup of coffee.
  2. Find the probability that the total volume of a randomly chosen small cup of coffee and a randomly chosen large cup of coffee is greater than 250 ml .