I have the following problem:
The resistance D has a normal distribution with expectation 11 and variance = 2. The force B has a normal distribution with expectation 9 and variance 1. Assume independence. What is the probability that the construction doesn't fail.
The answer is 0.8749
What I did already is draw the two normal distributions. I know that the construction will fail if the force is bigger than the resistance. So I have two intersecting normal distributions and I drew a vertical line through the intersection. Right of the line is the region where the resistance is bigger than the force.
But how do I calculate this region?
The random variable
$Y=(D-B)\sim N(2;3)$
so you can easily calculate
$\mathbb{P}[Y>0]=1-\Phi(\frac{-2}{\sqrt{3}})=1-\Phi(-1.15) \approx 87.49\%$