a) The random variable $X$ is normally distributed with mean $\mu $ and standard deviation $\sigma $. It is given that $3\mu = 7{\sigma ^2}$ and that $P\left( {X \gt 2\mu } \right) = 0.1016$. Find $\mu $ and $\sigma $.
b) It is given that $Y \sim N\left( {33,{\text{ }}21} \right)$. Find the value of $\alpha $ given that $P\left( {33 - \alpha \lt Y \lt 33 + \alpha } \right) = 0.5$.
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