5 The independent random variables \(X\) and \(Y\) have distributions \(\mathrm { N } \left( 30 , \sigma ^ { 2 } \right)\) and \(\mathrm { N } \left( 20 , \sigma ^ { 2 } \right)\) respectively. The random variable \(a X + b Y\), where \(a\) and \(b\) are constants, has the distribution \(\mathrm { N } \left( 410,130 \sigma ^ { 2 } \right)\).

1. Given that \(a\) and \(b\) are integers, find the value of \(a\) and the value of \(b\).
2. Given that \(\mathrm { P } ( X > Y ) = 0.966\), find \(\sigma ^ { 2 }\).