Normal distributions: distribution of sums

A straight rod is formed by connecting three sections A, B and C, each of which is manufactured on a different machine. The length of section A, in inches has a normal distributionwith mean20 and variance0.04. The length of section B, in inches, has a normal distribution with mean 14 and variance 0.01. The length of section C, in inches, has a normal distribution with mean 26 and variance 0.04. The three sections are joined so that there is an overlap of 2 inches at each connection. The rod is used in construction of an airplane wing if its total length is between 55.7 and 56.3. What is the probabilitythat the rod can be used?

This solution shows how to find the distribution of the sum of a set of normal random variables.