Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The random variable $X$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$.

(i)[3]

Using $5\sigma = 3\mu$, determine $P(X < 2\mu)$.

(ii)[3]

For a different link between $\mu$ and $\sigma$, it is stated that $P(X < \tfrac{1}{3}\mu) = 0.8524$. Write $\mu$ in terms of $\sigma$.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme.