Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

(a(i))[2]

The variable $X$ hours, representing the amount of sleep people get in one night, follows a normal distribution with mean $7.15$ hours and standard deviation $0.88$ hours. Find the probability that a person selected at random sleeps for under $8$ hours in one night.

(a(ii))[3]

Determine the value of $q$ for which $P(X < q) = 0.75$.

(b)[3]

The random variable $Y$ is distributed as $N(\mu, \sigma^2)$, with $2\sigma = 3\mu$ and $\mu \neq 0$. Find $P(Y > 4\mu)$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: The correct standardisation is $P\left(Z < \frac{8-7.15}{0.88}\right)$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI