a company manufactures video games with a current defect rate of 0.95%. to make sure as few defective video…

a company manufactures video games with a current defect rate of 0.95%. to make sure as few defective video games are delivered as possible, they are all tested before delivery. the test is 98% accurate at determining if a video game is defective. if 100,000 products are manufactured and delivered in a month, approximately how many defective products are expected to be delivered? 950 20 50 2,000

a company manufactures video games with a current defect rate of 0.95%. to make sure as few defective video games are delivered as possible, they are all tested before delivery. the test is 98% accurate at determining if a video game is defective. if 100,000 products are manufactured and delivered in a month, approximately how many defective products are expected to be delivered? 950 20 50 2,000

Answer

Explanation:

Step1: Calculate number of defective games

The defect - rate is 0.95%, so the number of defective games out of 100,000 is $100000\times0.0095 = 950$.

Step2: Calculate number of non - defective games

The number of non - defective games is $100000 - 950=99050$.

Step3: Calculate number of false negatives

The test is 98% accurate at detecting defective games. So the false - negative rate (the rate of defective games that pass the test) is $1 - 0.98=0.02$. The number of defective games that pass the test (false negatives) is $950\times0.02 = 19$.

Step4: Calculate number of false positives

The false - positive rate (the rate of non - defective games that are wrongly identified as defective) is also $1 - 0.98 = 0.02$. The number of non - defective games that fail the test (false positives) is $99050\times0.02=1981$. But we are interested in defective games that are delivered, so we ignore false positives.

Answer:

19 (closest to 20 among the given options)