- The queueing time, \(X\) minutes, of a customer at a till of a supermarket has probability density function
$$f ( x ) = \left\{ \begin{array} { c c }
\frac { 3 } { 32 } x ( k - x ) & 0 \leqslant x \leqslant k
0 & \text { otherwise }
\end{array} \right.$$
- Show that the value of \(k\) is 4
- Write down the value of \(\mathrm { E } ( X )\).
- Calculate \(\operatorname { Var } ( X )\).
- Find the probability that a randomly chosen customer's queueing time will differ from the mean by at least half a minute.