SOLUTION: A production process produces an item. On average 20% of all items produced are defective. Each item is inspected before being shipped. The inspector misclassifies an item 10% of t
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Question 1206541: A production process produces an item. On average 20% of all items produced are defective. Each item is inspected before being shipped. The inspector misclassifies an item 10% of the time, i.e. probability (classified/defective item) = Probability (classified defective/good item).
a. What proportions of the items will be classified defective.
b. Suppose that only items classified as good after inspection are shipped;
(i). What percentage of the items shipped are good.
(ii). What percentage of those shipped are good. Answer by Theo(13342) (Show Source):
80% of the total are actually good.
20% of the total are actually defective.
10% of the good are mis-classified as defective.
10% * 80% = 8% that are mis-classified as defective.
that leaves 80% minus 8% = 72% that are correctly classified as good.
10% of the defective are mis-classified as good.
10% * 20% = 2% that are mis-classified as good.
that leaves 20% minus 2% = 18% that are correctly classified as defective.
you have 72% that are correctly classified as good and 2% that are incorrectly classified as good for a total of 74% classified as good.
you have 18% that are correctly classified as defective and 8% that are incorrectly classified as defective for a total of 26% classified as defective.
totals look good.
80% actually good plus 20% actually defective = 100% total.
74% classified good plus 26% classified defective = 100% total.
this agrees with my original assessment.
let me know if you have any questions or concerns.
theo
