Three parts are assembled in series so that their critical dimensions x1, x2, and x3 add. The

Question:

Three parts are assembled in series so that their critical dimensions x1, x2, and x3 add. The dimensions of each part are normally distributed with the following parameters:
1 100,1  4, 2  75, 2  4, 3 75, 3 2 .
What is the probability that an assembly chosen at random will have a combined dimension in excess of 262?