Choose between scaling one value and adding independent values

$X\sim N(10,2^2)$ and $Y\sim N(12,3^2)$, independently. In N(mean, variance), the second parameter is variance.

$P(Y<10)=0.252$ to 3 significant figures.

$2X\sim N(2(10),2^2(2^2))=N(20,16)$. Thus $P(2X>25)=0.106$ to 3 significant figures.

$Y-X\sim N(12-10,3^2+2^2)=N(2,13)$. Hence $P(Y<X)=P(Y-X<0)=0.290$ to 3 significant figures.

$4X+5Y\sim N(4(10)+5(12),4^2(2^2)+5^2(3^2))=N(100,289)$. Therefore $P(4X+5Y>90)=0.722$ to 3 significant figures.

$X_1+X_2\sim N(10+10,2^2+2^2)=N(20,8)$. The upper-tail equation $P(X_1+X_2>x)=0.25$ gives x≈21.9 to 3 significant figures. This is the 75 th percentile of that sum distribution.