4 The weekly sales of petrol, \(X\) thousand litres, at a garage may be modelled by a continuous random variable with probability density function given by
$$f ( x ) = \begin{cases} c & 25 \leqslant x \leqslant 45
0 & \text { otherwise } \end{cases}$$
where \(c\) is a constant. The weekly profit, in \(\pounds\), is given by \(( 400 \sqrt { X } - 240 )\).
- Obtain the value of \(c\).
- Find the expected weekly profit.
- Find the probability that the weekly profit exceeds \(\pounds 2000\).