The variable \(X\) has the distribution \(\mathrm { N } ( 20,9 )\).
(a) Find \(\mathrm { P } ( X > 25 )\).
(b) Given that \(\mathrm { P } ( X > a ) = 0.2\), find \(a\).
(c) Find \(b\) such that \(\mathrm { P } ( 20 - b < X < 20 + b ) = 0.5\).
The variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \frac { \mu ^ { 2 } } { 9 } \right)\). Find \(\mathrm { P } ( Y > 1.5 \mu )\).