The random variable \(X\) is normally distributed with mean 82 and standard deviation 7.4. Find the value of \(q\) such that \(\mathrm { P } ( 82 - q < X < 82 + q ) = 0.44\).
The random variable \(Y\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\). It is given that \(5 \mu = 2 \sigma ^ { 2 }\) and that \(\mathrm { P } \left( Y < \frac { 1 } { 2 } \mu \right) = 0.281\). Find the values of \(\mu\) and \(\sigma\).