The Quality Control Manager for NKA Inc

question 54

Short Answer

The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁), 50 percent chance that the lot is fair quality (S₂), and 20 percent chance that the lot is good quality (S₃). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars.
Based on historical data, if the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is defective. Based on this additional information, determine the revised (posterior) probabilities for each of the three states of nature.

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Definitions:

Slaves Freed

The act of emancipating or the state of being emancipated from slavery; particularly refers to historical events such as the Emancipation Proclamation or the end of the Civil War in the United States.

Seneca Falls Convention

The first women's rights convention, held in 1848 in Seneca Falls, New York, marking the beginning of the organized women's suffrage movement in the United States.

Declaration of Sentiments

A document signed in 1848 at the first women's rights convention that outlined the rights American women should be entitled to as citizens.

Grimké Sisters

Sarah and Angelina Grimké were 19th-century American abolitionists and advocates of women's rights, known for their pioneering work in both movements and facing significant opposition for their activism.