An inspector working for a manufacturing company has a 9 9

An inspector working for a manufacturing company has a 9 9 % chance of correctly identifying defective items and a 0 .5 % chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 1 .2% of nonconforming items. Round your answers to five decimal places (e.g. 98.76543). What is the probability that an item selected for inspection is classified as defective? If an item selected at random is classified as nondefective, what is the probability that it is indeed good?

Solution

a)

probability that item selected is defective

= probability of correctly identifying defective * probability of non conforming item

= 99% * 1.2%

= 1.188%

b)

probability of that it is indeed good

= probability of correctly identifying good * probability of good item

= (100%-0.5%) * (100%-1.2%)

= 93.86%