4. The length of a telephone call made to a company is denoted by the continuous random variable \(T\). It is modelled by the probability density function
$$\mathrm { f } ( t ) = \left\{ \begin{array} { c l }
k t & 0 \leqslant t \leqslant 10
0 & \text { otherwise }
\end{array} \right.$$
- Show that the value of \(k\) is \(\frac { 1 } { 50 }\).
- Find \(\mathrm { P } ( T > 6 )\).
- Calculate an exact value for \(\mathrm { E } ( T )\) and for \(\operatorname { Var } ( T )\).
- Write down the mode of the distribution of \(T\).
It is suggested that the probability density function, \(\mathrm { f } ( t )\), is not a good model for \(T\).
- Sketch the graph of a more suitable probability density function for \(T\).