CAIE S2 2010 June — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2010
SessionJune
TopicLinear combinations of normal random variables
TypeTotal journey time probabilities

6 Yu Ming travels to work and returns home once each day. The times, in minutes, that he takes to travel to work and to return home are represented by the independent random variables \(W\) and \(H\) with distributions \(\mathrm { N } \left( 22.4,4.8 ^ { 2 } \right)\) and \(\mathrm { N } \left( 20.3,5.2 ^ { 2 } \right)\) respectively.
  1. Find the probability that Yu Ming's total travelling time during a 5-day period is greater than 180 minutes.
  2. Find the probability that, on a particular day, Yu Ming takes longer to return home than he takes to travel to work.