12 The continuous random variable \(X\) has cumulative distribution function given by
$$F ( x ) = \begin{cases} 0 & x < 0
k \left( a x - 0.5 x ^ { 2 } \right) & 0 \leqslant x \leqslant a
1 & x > a \end{cases}$$
where \(a\) and \(k\) are positive constants.
- Determine the median of \(X\) in terms of \(a\).
- Given that \(a = 10\), determine the probability that \(X\) is within one standard deviation of its mean.