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