Higbee Manufacturing Corp

question 61

Short Answer

Higbee Manufacturing Corp.has recently received 5 cases of a certain part from one of its suppliers.The defect rate for the parts is normally 5%,but the supplier has just notified Higbee that one of the cases shipped to them has been made on a misaligned machine that has a defect rate of 97%.So the plant manager selects a case at random and tests a part.
a.What is the probability that the part is defective?
b.Suppose the part is defective, what is the probability that this is from the case made on the misaligned machine?
c.After finding that the first part was defective, suppose a second part from the case is tested. However, this part is found to be good. Using the revised probabilities from part (b) compute the new probability of these parts being from the defective case.
d.Do you think you would obtain the same posterior probabilities as in part (c) if the first part was not found to be defective but the second part was?
e.Suppose, because of other evidence, the plant manager was 80% certain this case was the one made on the misaligned machine. How would your answer to part (b) change?

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Definitions:

Technical Capability

Refers to the skills, knowledge, tools, and processes that enable an organization to effectively design, produce, and deliver products or services.

Government Regulation

Laws and rules established by governments to control or manage certain activities, behaviors, or industries for the protection and benefit of society.

Consumer Products

Goods bought and used by consumers for personal or household purposes, including non-durable goods like food or durable goods like appliances.

Organizations

Entities comprised of multiple people working together towards a common goal, structured in a specific way to achieve objectives.