2 Each day at the gym, Sarah completes three runs. The distances, in metres, that she completes in the three runs have the independent distributions \(W \sim \mathrm {~N} ( 1520,450 ) , X \sim \mathrm {~N} ( 2250,720 )\) and \(Y \sim \mathrm {~N} ( 3860,1050 )\). Find the probability that, on a particular day, \(Y\) is less than the total of \(W\) and \(X\).

2 Each day at the gym, Sarah completes three runs. The distances, in metres, that she completes in the three runs have the independent distributions $W \sim \mathrm {~N} ( 1520,450 ) , X \sim \mathrm {~N} ( 2250,720 )$ and $Y \sim \mathrm {~N} ( 3860,1050 )$.

Find the probability that, on a particular day, $Y$ is less than the total of $W$ and $X$.\\

\hfill \mbox{\textit{CAIE S2 2020 Q2}}