Edexcel S3 2014 June — Question 4

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2014
SessionJune
TopicLinear combinations of normal random variables
TypeTwo or more different variables

  1. The random variable \(A\) is defined as
$$A = B + 4 C - 3 D$$ where \(B\), \(C\) and \(D\) are independent random variables with $$B \sim \mathrm {~N} \left( 6,2 ^ { 2 } \right) \quad C \sim \mathrm {~N} \left( 7,3 ^ { 2 } \right) \quad D \sim \mathrm {~N} \left( 4,1.5 ^ { 2 } \right)$$ Find \(\mathrm { P } ( A < 45 )\)