Normal distribution help

I am lost.

How do I find this:

Let X ~ N(4, 4) and Y ~ N(1, 4) be two independent random variables. Using the normal distribution
table …nd the following probabilities:

P(abs(X + Y - 5) > 1)



P(4 < X < 8 or Y < 1)


I know how to use the z table and how to find the probabilities when it is just like x>2, but cant figure out how to do it with these. help please

Since X and Y are independent, X+Y ~ N(5, 8)
P(abs(X + Y - 5) > 1) = P[X+Y-5 <= -1] + P[X+Y-5 >= 1]
= P[X+Y <= 4] + P[X+Y >= 6]
= P[Z <= -0.35] + P[Z >= 0.35
= 0.7264

P(4 < X < 8 or Y < 1) = P(4 < X < 8) + P(Y < 1) - P(4 < X < 8)P(Y < 1)=0.7386