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

---

Definitions:

Incentives

External or internal rewards designed to encourage specific actions or behaviors.

Referent Power

A form of influence based on the leader's personal characteristics, where followers identify with and want to emulate them.

Reward Power

The influence and control one has over others based on the ability to grant rewards or benefits.

Organizational Power

The ability of individuals or groups in an organization to influence decisions, control resources, and direct the actions of others.