5. The random variable \(X\) has cumulative distribution function given by
$$F ( x ) = \left\{ \begin{array} { l r }
0 & x < 0
\frac { 1 } { 100 } \left( a x ^ { 3 } + b x ^ { 2 } + 15 x \right) & 0 \leqslant x \leqslant 5
1 & x > 5
\end{array} \right.$$
Given that \(\mathrm { E } \left( X ^ { 2 } \right) = 6.25\)
- show that \(6 a + b = 0\)
- find the value of \(a\) and the value of \(b\)
- find \(\mathrm { P } ( 3 \leqslant X \leqslant 7 )\)