4. A continuous random variable \(X\) has cumulative distribution function
$$F ( x ) = \left\{ \begin{array} { l r }
0 & x < 0
\frac { 1 } { 4 } x & 0 \leqslant x \leqslant 1
\frac { 1 } { 20 } x ^ { 4 } + \frac { 1 } { 5 } & 1 < x \leqslant d
1 & x > d
\end{array} \right.$$
- Show that \(d = 2\)
- Find \(\mathrm { P } ( X < 1.5 )\)
- Write down the value of the lower quartile of \(X\)
- Find the median of \(X\)
- Find, to 3 significant figures, the value of \(k\) such that \(\mathrm { P } ( X > 1.9 ) = \mathrm { P } ( X < k )\)