CAIE S2 2024 March — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2024
SessionMarch
TopicLinear combinations of normal random variables
TypeTwo or more different variables

4 Each year a transport firm uses \(X\) litres of gasoline and \(Y\) litres of diesel fuel, where \(X\) and \(Y\) have the independent distributions \(X \sim \mathrm {~N} ( 10700,950 ) ^ { 2 }\) and \(Y \sim \mathrm {~N} \left( 13400,1210 ^ { 2 } \right)\).
  1. Find the probability that in a randomly chosen year the firm uses more gasoline than diesel fuel.
    The costs per litre of gasoline and diesel fuel are \\(0.80 and
    )0.85 respectively.
  2. Find the probability that the total cost of gasoline and diesel fuel in a randomly chosen year is between \(
    ) 20000\( and \)\\( 22000\).