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

question 9

Essay

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,determine the revised (posterior)probabilities for each of the three states of nature.

Evaluate the prevalence of unplanned pregnancies in the United States.

Historical perspective on life expectancy changes over years for women.

Identify the leading causes of death in women today.

Comprehend the prevalence and impact of sexually transmitted infections among young adults.

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Definitions:

Variance

A measure of the spread between numbers in a dataset, expressing how much the numbers differ from the average value.

Significance Level

The probability of rejecting the null hypothesis in a statistical test when it is true, used as a threshold to gauge the strength of the evidence against the null hypothesis.

Standard Deviation

Measures the amount of variance or dispersion of a set of values; a low standard deviation indicates that the values are close to the mean.

Delivery Times

The duration taken for goods or services to be transported from the supplier to the recipient.