You are a consultant to a company that manufactures components for cell phones. One of the components the company manufactures has a​ 4% failure rate. Design changes have improved the quality of the component. A test of 50 of the new components found that only one of the new components is defective.
a. Before the design​ improvements, what was the probability​ that, among 50 of the​ items, at most one of the items was​ defective?
b. Is it reasonable to conclude that the new components have a lower failure rate​ than 4%?
c. Would you recommend further testing to determine whether the new parts have a lower failure rate than​ 4%? Explain.