The random variable $X$ is normally distributed with mean $\mu $ and standard deviation $\frac{1}{4}\mu $. It is given that $P\left( {X \gt 20} \right) = 0.04$.
a) Find $\mu $.
b) Find $P\left( {10 \lt X \lt 20} \right)$.
c) 250 independent observations of $X$ are taken. Find the probability that at least 235 of them are less than 20.
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