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

question 37

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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.  States of Nature  Decision S1 S2 S3 Accept 203090 Further analyze 607015 Reject 805030\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?

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Definitions:

Advertising Budget

The amount of money allocated by a business for activities related to the promotion and advertising of its products or services.

Monthly Sales

The total revenue generated from sales operations within a specific month.

Sales Commissions

A portion of the sale price paid to salespersons as a reward for their sales efforts, typically a percentage of the sales they generate.

Monthly Sales

The total revenue generated from the sale of goods or services by a company within a month.

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