One piece of pvc pipe is to be inserted inside the another piece. the length of the first piece is normally distributed with mean 20 inch and sd 0.5 inch. the length of the second piece is normally distributed with mean 15 inch and sd 0.4 inch. the amount of overlap is normally distributed with mean 1 inch and sd 0.1 inch. assuming that the lengths and the amount of overlap are independent of one another, what is the probability that the total length after insertion is between 34.5 inch and 35 inch?