CAIE S2 2005 June — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2005
SessionJune
TopicLinear combinations of normal random variables
TypeLinear transformation to achieve target parameters

1 Exam marks, \(X\), have mean 70 and standard deviation 8.7. The marks need to be scaled using the formula \(Y = a X + b\) so that the scaled marks, \(Y\), have mean 55 and standard deviation 6.96. Find the values of \(a\) and \(b\).