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