CAIE S1 2010 November — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionNovember
TopicNormal Distribution
TypeDirect comparison of probabilities

5 The distance the Zotoc car can travel on 20 litres of fuel is normally distributed with mean 320 km and standard deviation 21.6 km . The distance the Ganmor car can travel on 20 litres of fuel is normally distributed with mean 350 km and standard deviation 7.5 km . Both cars are filled with 20 litres of fuel and are driven towards a place 367 km away.
  1. For each car, find the probability that it runs out of fuel before it has travelled 367 km .
  2. The probability that a Zotoc car can travel at least \(( 320 + d ) \mathrm { km }\) on 20 litres of fuel is 0.409 . Find the value of \(d\).