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

question 50

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 accept state?

• A)24
• B)52
• C)18
• D)39
• E)78

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Definitions:

Anorexia Nervosa

Exaggerated concern with being overweight that leads to inadequate food intake and often excessive exercising; can lead to severe weight loss and even starvation.

Severe Weight Loss

A significant and rapid decrease in body weight, often associated with diseases, disorders, or extreme dietary practices.

Starvation

A severe deficiency in caloric energy, nutrient, and vitamin intake, leading to extreme hunger, weight loss, and possibly death if not addressed.

Masculinization

Process by which exposure to androgens (male sex hormones) alters the brain, rendering it identifiably male.