The probability density function for \(X\) is
\(f_X(x)=\begin{cases}\dfrac1\beta e^{-x/\beta}&\text{for }x>0\\\\0&\text{otherwise}\end{cases}\)
where \(\beta\) is the scale parameter of the distribution, which for exponential distributions is also the mean.
The probability is then
\(\mathbb P(15
\(=\displaystyle\frac1{25}\int_{15}^{35}e^{-x/25}\,\mathrm dx\)
\(=\displaystyle-e^{-x/25}\bigg|_{x=15}^{x=35}\)
\(=e^{-15/25}-e^{-35/25}\approx0.3022\)
