4 The cumulative distribution function of the continuous random variable \(X\) is given by
\(\mathrm { F } ( x ) = \begin{cases} 0 & x < 0 ,
k \left( 12 x - x ^ { 2 } \right) & 0 \leqslant x \leqslant 2 ,
1 & x > 2 , \end{cases}\) where \(k\) is a constant.

1. Show that \(k = 0.05\).
2. Find \(\mathrm { P } ( 1 \leqslant X \leqslant 1.5 )\).
3. Find the median of \(X\), correct to 3 significant figures.
4. Find which of the median, mean and mode of \(X\) is the largest of the three measures of central tendency.