3 The waiting time, \(T\) weeks, for a particular operation at a hospital has probability density function given by $$f ( t ) = \begin{cases} \frac { 1 } { 2500 } \left( 100 t - t ^ { 3 } \right) & 0 \leqslant t \leqslant 10
0 & \text { otherwise } \end{cases}$$

1. Given that \(\mathrm { E } ( T ) = \frac { 16 } { 3 }\), find \(\operatorname { Var } ( T )\).
2. \(10 \%\) of patients have to wait more than \(n\) weeks for their operation. Find the value of \(n\), giving your answer correct to the nearest integer.