CAIE S2 2013 November — Question 7

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2013
SessionNovember
TopicLinear combinations of normal random variables
TypeDirect comparison of two variables

7 Kieran and Andreas are long-jumpers. They model the lengths, in metres, that they jump by the independent random variables \(K \sim \mathrm {~N} ( 5.64,0.0576 )\) and \(A \sim \mathrm {~N} ( 4.97,0.0441 )\) respectively. They each make a jump and measure the length. Find the probability that
  1. the sum of the lengths of their jumps is less than 11 m ,
  2. Kieran jumps more than 1.2 times as far as Andreas.