CAIE S2 2006 June — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2006
SessionJune
TopicLinear combinations of normal random variables
TypeExpectation and variance with context application

2 A mathematics module is assessed by an examination and by coursework. The examination makes up \(75 \%\) of the total assessment and the coursework makes up \(25 \%\). Examination marks, \(X\), are distributed with mean 53.2 and standard deviation 9.3. Coursework marks, \(Y\), are distributed with mean 78.0 and standard deviation 5.1. Examination marks and coursework marks are independent. Find the mean and standard deviation of the combined mark \(0.75 X + 0.25 Y\).