The random variable \(X\) has probability density function f given by
\[f(x)=\left\{\begin{array}{ll}
\frac{1}{30}\left(\frac{8}{x^{2}}+3 x^{2}-14\right) & 2 \leqslant x \leqslant 4 \\
0 & \text { otherwise. }
\end{array}\right.\]
(i) Find the distribution function of \(X\).

The random variable \(Y\) is defined by \(Y=X^{2}\).
(ii) Find the probability density function of \(Y\).

(iii) Find the value of \(y\) such that \(\mathrm{P}(Y<y)=0.8\).