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

question 37

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 further analyze state?

• A)44
• B)52
• C)18
• D)39
• E)48

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Definitions:

NHL

Stands for Non-Hodgkin Lymphoma, a type of cancer that affects the lymphatic system.

Malignant Cancer

A type of cancer that is invasive and can spread to other parts of the body (metastasize).

Neoplasms

Abnormal growths of tissue, which can be benign or malignant (cancerous), arising from the uncontrolled proliferation of cells.

Arachnoid Layer

The middle layer of the three meninges that cover the brain and spinal cord, providing a protective barrier.