7. The time, in hours, taken to run the London marathon is modelled by a continuous random variable \(T\) with the probability density function $$f ( t ) = \begin{cases} c ( t - 2 ) & 2 \leq t < 4
\frac { 2 c ( 7 - t ) } { 3 } & 4 \leq t \leq 7
0 & \text { otherwise } \end{cases}$$

1. Sketch the function \(\mathrm { f } ( t )\), and show that \(c = \frac { 1 } { 5 }\).
2. Calculate the median value of \(T\).
3. Make two critical comments about the model.