(a)[3]
The random variable $X$ has a normal distribution with mean $82$ and standard deviation $7.4$. Determine the value of $q$ for which $P(82-q < X < 82+q) = 0.44$.
(b)[4]
The random variable $Y$ follows a normal distribution with mean $\mu$ and standard deviation $\sigma$. You are told that $5\mu = 2\sigma^2$ and also that $P\left(Y < \tfrac{1}{2}\mu\right) = 0.281$. Determine the values of $\mu$ and $\sigma$.