A Machine Is Used in a Production Process

question 101

Short Answer

A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items.
a.An item from the production line is selected. What is the probability that the selected item is non-defective?
b.Given that the selected item is non-defective, what is the probability that the machine is set up correctly?

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Definitions:

Postcategorization

The process or practice of reevaluating and possibly redefining categorizations, often in the context of social identities or classifications.

Precategorization

The early or initial process of classifying or sorting objects, ideas, or information into categories, often before more detailed analysis.

Robbers Cave

A landmark social psychology experiment by Muzafer Sherif that illustrated how intergroup conflict can arise from competition for resources and how it can be overcome by working towards shared goals.

Superordinate Goals

Shared objectives that transcend individual or group interests, requiring cooperative efforts to achieve.