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

question 66

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 not defective.Based on this additional information,what is the revised (posterior) probability for the reject state?

• A)24
• B)52
• C)18
• D)39
• E)78

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Definitions:

Conflict Escalation

The process by which disputes or conflicts grow in severity and magnitude, potentially becoming more difficult to resolve.

Conflict De-escalation

Strategies or actions aimed at reducing the intensity, hostility, or severity of a dispute to prevent further escalation.

Routine Interaction

Regular and repetitive interactions that occur in a set pattern among individuals or groups within social settings.

Prisoner's Dilemma

A standard example of a game analyzed in game theory that shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so.