11 The random variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\).
- Find \(\mathrm { P } ( Y > \mu - \sigma )\).
- Given that \(\mathrm { P } ( Y > 45 ) = 0.2\) and \(\mathrm { P } ( Y < 25 ) = 0.3\), determine the values of \(\mu\) and \(\sigma\).
The random variables \(U\) and \(V\) have the distributions \(\mathrm { N } ( 10,4 )\) and \(\mathrm { N } ( 12,9 )\) respectively.
- It is given that \(\mathrm { P } ( U < b ) = \mathrm { P } ( V > c )\), where \(b > 10\) and \(c < 12\).
Determine \(b\) in terms of \(c\).