May/June 2026 Paper 62

Each week, Birgitte takes three train journeys. The times, in minutes, for these journeys have the independent distributions $A\sim \mathrm{N}(28,15)$, $B\sim \mathrm{N}(23,8)$ and $C\sim \mathrm{N}(99,24)$. For a randomly chosen week, find $\mathrm{P}(C>2(A+B))$.