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?\n2,000\n950\n20\n50

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?\n2,000\n950\n20\n50

Answer

Explanation:

Step1: Calculate number of defective products

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

Step2: Calculate number of non - defective products

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

Step3: Calculate number of false - negatives

The test is 98% accurate at determining if a video game is defective. So the false - negative rate (defective products that pass the test) is $1 - 0.98=0.02$. The number of defective products that pass the test is $950\times0.02 = 19$.

Step4: Calculate number of false - positives

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

Answer:

19 (closest to 20) so the answer is C. 20