Standardise tails of three independent normal variables
X,Y,Z are mutually independent normal variables. In N(μ,σ²), the second parameter is the variance. All three displayed weights are nonzero. Find the combined distribution parameters, standardise the boundary and calculate the requested tail. Give exact parameters and a probability to four decimal places
\[X\sim N(4,1),\quad Y\sim N(0,4),\quad Z\sim N(4,4)\]
\[W=(1)X+(-1)Y+(-1)Z+(-3),\qquad \Pr(W<-\frac{3}{4})\]