October 2021 Paper 2 Q8

8 The Normal variable \(X\) is transformed to the Normal variable \(Y\).

The transformation is \(y = a + bx\), where \(a\) and \(b\) are positive constants.

You are given that \(X \sim N(42, 6.8)\) and \(Y \sim N(57.2, 11.492)\).

Determine the values of \(a\) and \(b\). [4]