Help me to find probability P(X1+4X2>12)=

Question

X~Normal (0, 4) for i= 1,2,3,4. Assume they are independenr

Answer 1

if X ~ N(a,z), kX ~ N(ka,k^2z)

If X ~ N(a,b), Y ~ N(c,d), and X and Y are independent, X + Y ~ N(a+c,b+d)

Thus, if X ~ N(0,4) and X1 and X2 are samples from this distribution,

X1 ~ N(0, 4), X2 ~ N(0, 4), 4X2 ~ N(0, 64), and

X1 + 4X2 ~ N(0, 68)

Then, P(X1 + 4X2 > 12) = 1 - Φ(12/sqrt(68) = from Excel,1 - normsdist(12/sqrt(68)) = .0728