(i)[3]
Calculate $\mu$.
(ii)[3]
Calculate $\mathrm{P}(10 < X < 20)$.
(iii)[5]
$250$ independent observations of $X$ are taken. Calculate the probability that at least $235$ of them are less than $20$.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Let $X$ be normally distributed with mean $\mu$ and standard deviation $\tfrac{1}{4}\mu$. It is known that $\mathrm{P}(X > 20) = 0.04$.