A defense contractor developed a new welding process of high-strength metal for use in constructing submarines. The new process was used and the resulting welds were tested using a specialized nondestructive testing method. The testing produced a reliability level of 99.9% for the length of welds. The submarine construction is expected to require 10,000 ft of welding at various locations of the submarine hull. Determine the expected length of defective welds in the 10,000 ft of welds.

Modeling each 1 ft of weld as a Bernoulli trial, what is the probability of having 1 ft or more of defective weld length based on nondestructive examination of sample welds of 500 ft? What is this probability if the sample size is varied from 10 to 10,000 ft as follows: 10, 20, 50, 100, 1000, 5000, and 10,000? Plot your results. Can you recommend a sample size?