Question

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.

Answer 1

a. Before the design improvements, the probability that at most one of the items was defective was 0.7233.

b. Yes, it is reasonable to conclude that the new components have a lower failure rate than 4%.

c. Yes, I would recommend further testing to determine whether the new parts have a lower failure rate than 4%. This is because one sample of 50 items is not enough to determine that the new components have a statistically significant lower failure rate. Further testing should be done to give more conclusive evidence.