Write $\bar s>0$ for the <mean> in minutes. An <exponential distribution> with that <mean> has rate $1/\bar s$, so its <probability density function> is
$$
\boxed{f_S(s)=\begin{cases}\bar s^{-1}e^{-s/\bar s},&s\geq0,\\0,&s<0.\end{cases}}
$$
The density has units of inverse minutes, ensuring that its integral is a dimensionless <probability>.

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 12 / a / Solution

 Solution (source code)