Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The duration, in minutes, that students need in order to finish a test is represented by the random variable $X$ with probability density function $f(x)=\begin{cases}-\frac{3}{4}(x-3)(x-5), & 3\leq x\leq 5,\\0, & \text{otherwise}.\end{cases}$
(a)[4]
Find the probability that a student selected at random needs more than $4.5$ minutes to finish the test.
(b)[1]
Write down the median value of $X$.
(c)[2]
Without carrying out any integration, use your answer to part (a) to find $\mathrm{P}(3.5 < X < 4.5)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$f(x)=-\frac{3}{4}(x^2-8x+15)$ and start the integration” …