The Quality Control Manager for the NKA Inc Based on Historical Data,if the Lot Is of Poor Quality,40

question 95

Multiple Choice

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1) ,further analyze (alternative 2) ,or reject (alternative 3) the shipment (lot) of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S₁) ,50% chance that the lot is fair quality (S₂) ,and 20% 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. $$\begin{array} { l c c c } & { \text { States of Nature } } \\\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \\\text { Accept } & 20 & 30 & 90 \\\text { Further analyze } & 60 & 70 & 15 \\\text { Reject } & 80 & 50 & 30\end{array}$$
Based on historical data,if the lot is of poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting one unit,the manager determines that the unit is defective.Based on this additional information,what is the revised (posterior) probability for the reject state?

• A)44
• B)52
• C)18
• D)08
• E)48

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Definitions:

Inflammation

A localized physical condition in which part of the body becomes reddened, swollen, hot, and often painful, especially as a reaction to injury or infection.

Buccal

Relating to the cheek or the mouth cavity.

Cheilosis

A condition that causes inflammation and cracking of the lips, often due to a deficiency of riboflavin (vitamin B2).

Celiac

Referring to celiac disease, a medical condition where the ingestion of gluten leads to damage in the small intestine.