7. The queuing time in minutes, \(X\), of a customer at a post office is modelled by the probability density function $$f ( x ) = \begin{cases} k x \left( 81 - x ^ { 2 } \right) & 0 \leqslant x \leqslant 9
0 & \text { otherwise } \end{cases}$$

1. Show that \(k = \frac { 4 } { 6561 }\). Using integration, find
2. the mean queuing time of a customer,
3. the probability that a customer will queue for more than 5 minutes. Three independent customers shop at the post office.
4. Find the probability that at least 2 of the customers queue for more than 5 minutes.