A continuous random variable \(X\) has the following probability density function
\(g(x) = \begin {cases}
\dfrac{x-1}{20} &\ \ 1 \leq x < 6 \\
\\
\dfrac{9-x}{12} &\ \ 6 \leq x < 9 \\
\\ 0 &\ \ \ \text{elsewhere}
\end{cases}\)
The value of \(\large k\) such that \(\text{Pr}(X<k)=0.35\) is
- \(\sqrt{14}-1\)
- \(\sqrt{14}+1\)
- \(\sqrt{15}-1\)
- \(\sqrt{15}+1\)
- \(1-\sqrt{15}\)