4 An archer fires arrows at a circular target of radius 50 cm . The distance in cm that an arrow lands from the centre of the target is modelled by the random variable \(X\), with probability density function given by
\(f ( x ) = \begin{cases} a x & 0 \leqslant x \leqslant 50 ,
0 & \text { otherwise, } \end{cases}\)
where \(a\) is a constant.
- Determine the value of \(a\).
- Determine the probability that an arrow will land within 5 cm of the centre of the target.
- Determine the median distance from the centre of the target that an arrow will land.