One piece of PVC is to be inserted inside another piece. The length of the first piece is normally distributed with a mean value of 20 inches and a standard deviation of 0.5 inches. The length of the second pipe is normally distributed with a mean of 15 inches and a standard deviation of 0.4 inches. The amount of overlap is normally distributed with a mean of 1 inch and a standard deviation of 0.2 inches. Assuming the lengths and the amount of overlap are independent of each other, what is the probability that the total length after insertion is between 34.5 and 35 inches?