Question

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?
20
50
2,000
950

Explanation:

Step1: Find number of defective products initially

The defect rate is \(0.95\%\), so for \(100,000\) products, the number of defective products is \(100000\times0.95\% = 100000\times\frac{0.95}{100}=950\).

Step2: Find the percentage of defective products that pass the test (are delivered)

The test is \(98\%\) accurate, so the percentage of defective products that are not detected (and thus delivered) is \(100\% - 98\%=2\% = 0.02\).

Step3: Calculate the number of defective products delivered

Multiply the number of defective products by the percentage that pass the test: \(950\times0.02 = 19\approx20\).

Answer:

20