CAIE S2 2010 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2010
SessionJune
TopicLinear combinations of normal random variables
TypeDirect comparison of two variables

4 The weekly distance in kilometres driven by Mr Parry has a normal distribution with mean 512 and standard deviation 62. Independently, the weekly distance in kilometres driven by Mrs Parry has a normal distribution with mean 89 and standard deviation 7.4.
  1. Find the probability that, in a randomly chosen week, Mr Parry drives more than 5 times as far as Mrs Parry.
  2. Find the mean and standard deviation of the total of the weekly distances in miles driven by Mr Parry and Mrs Parry. Use the approximation 8 kilometres \(= 5\) miles.