Age 16 to 18 Challenge Level:
The area under the graph of the probability density function
between $x=a$ and $x=b$ gives the probability that the outcome is
between $a$ and $b$ so the total area under the graph must be $1$,
in this example for $x$ between $0$ and $3$.
To find the median we have to find the value $t$ such that the area
under the graph for $0\leq x \leq t$ is $0.5$. You will have to
find the roots of a cubic equation (which you should be able to
factorise) in this example and then identify the root which lies in
the required interval.