6 The time, \(T\) hours, spent by people on a visit to a museum has probability density function $$\mathrm { f } ( t ) = \begin{cases} k t \left( 16 - t ^ { 2 } \right) & 0 \leqslant t \leqslant 4
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.

1. Show that \(k = \frac { 1 } { 64 }\).
2. Calculate the probability that two randomly chosen people each spend less than 1 hour on a visit to the museum.
3. Find the mean time spent on a visit to the museum.