Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 2 / 14 / a / i / Solution

The probability density is symmetric about $300\mathrm{mL}$, vanishes at $270$ and $330\mathrm{mL}$, and has its single maximum $\pi /(120\mathrm{mL})$ at $300\mathrm{mL}$. It is zero outside that interval. Its area is one: with the dimensionless change of variablesnormalization is $\frac{1}{2}{\int }_{-\pi /2}^{\pi /2}\cos xdx=1$.