Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

(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 $P(33 - a < Y < 33 + a) = 0.5$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: A standardising attempt leading to $z > \frac{2\mu-\mu}{\sigma} = \frac{\mu}{\sigma} = \frac{7\sigma^2}{3\sigma}$

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