12 The cumulative distribution function of the continuous random variable \(X\) is given by
\(F ( x ) = \begin{cases} 0 & x < 20 ,
a \left( x ^ { 2 } + b x + c \right) & 20 \leqslant x \leqslant 30 ,
1 & x > 30 , \end{cases}\)
where \(a\), \(b\) and \(c\) are constants.
You are given that \(\mathrm { P } ( X < 25 ) = \frac { 11 } { 24 }\).
- Find \(\mathrm { P } ( X > 27 )\).
- Find the 90th percentile of \(X\).