CAIE S2 2019 November — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2019
SessionNovember
TopicLinear combinations of normal random variables
TypeSingle sum threshold probability

5 The masses, in grams, of large boxes of chocolates and small boxes of chocolates have the distributions \(\mathrm { N } ( 325,6.1 )\) and \(\mathrm { N } ( 167,5.6 )\) respectively.
  1. Find the probability that the total mass of 10 randomly chosen large boxes of chocolates is less than 3240 g .
  2. Find the probability that the mass of a randomly chosen large box of chocolates is more than twice the mass of a randomly chosen small box of chocolates.