(a)[4]
The random variable $X$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. You are told that $3\mu = 7\sigma^2$ and that $P(X > 2\mu) = 0.1016$. Find $\mu$ and $\sigma$.
(b)[4]
It is given that $Y \sim N(33, 21)$. Find the value of $a$ when $P(33 - a < Y < 33 + a) = 0.5$.