7 The time, \(T\) hours, that the supporters of Bracken Football Club have to queue in order to obtain their Cup Final tickets has the following probability density function. $$\mathrm { f } ( t ) = \begin{cases} \frac { 1 } { 5 } & 0 \leqslant t < 3
\frac { 1 } { 45 } t ( 6 - t ) & 3 \leqslant t \leqslant 6
0 & \text { otherwise } \end{cases}$$

1. Sketch the graph of f.
2. Write down the value of \(\mathrm { P } ( T = 3 )\).
3. Find the probability that a randomly selected supporter has to queue for at least 3 hours in order to obtain tickets.
4. Show that the median queuing time is 2.5 hours.
5. Calculate P (median \(< T <\) mean).