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 the normal distribution with mean 20 and variance 0.04. The length of section B, in inches, has the normal distribution with mean 14 and variance 0.01. The length of section C, in inches, has the normal distribution with mean 26 and variance 0.04. As indicated in Fig. 5.6, the three sections are joined so that there is an overlap of 2 inches at each connection. Suppose that the rod can be used in the construction of an airplane wing if its total length in inches is between 55.7 and 56.3.What is the probability that the rod can be used?
Figure 5.6 Sections of the rod in Exercise 9.
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