CAIE S2 2022 November — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionNovember
TopicLinear combinations of normal random variables
TypeSum versus sum comparison

6 The masses, in grams, of small and large bags of flour have the distributions \(\mathrm { N } ( 510,100 )\) and \(\mathrm { N } ( 1015,324 )\) respectively. André selects 4 small bags of flour and 2 large bags of flour at random.
  1. Find the probability that the total mass of these 6 bags of flour is less than 4130 g .
  2. Find the probability that the total mass of the 4 small bags is more than the total mass of the 2 large bags.