CAIE S2 2014 November — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2014
SessionNovember
TopicLinear combinations of normal random variables
TypeMixed sum threshold probability

4 The masses, in grams, of tomatoes of type \(A\) and type \(B\) have the distributions \(\mathrm { N } \left( 125,30 ^ { 2 } \right)\) and \(\mathrm { N } \left( 130,32 ^ { 2 } \right)\) respectively.
  1. Find the probability that the total mass of 4 randomly chosen tomatoes of type \(A\) and 6 randomly chosen tomatoes of type \(B\) is less than 1.5 kg .
  2. Find the probability that a randomly chosen tomato of type \(A\) has a mass that is at least \(90 \%\) of the mass of a randomly chosen tomato of type \(B\).