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? 50 20 950 2,000
Answer
Explanation:
Step1: Calculate number of defective products before test
The defect - rate is 0.95%, and 100000 products are manufactured. So the number of defective products is $100000\times0.95%=100000\times\frac{0.95}{100}=950$.
Step2: Calculate number of non - defective products
The number of non - defective products is $100000 - 950=99050$.
Step3: Calculate number of defective products mis - classified as non - defective
The test is 98% accurate at determining if a product is defective. So the percentage of defective products mis - classified as non - defective is $(1 - 98%)=2%$. The number of defective products mis - classified as non - defective is $950\times2%=950\times\frac{2}{100}=19$.
Step4: Calculate number of non - defective products mis - classified as defective
The percentage of non - defective products mis - classified as defective is also $(1 - 98%) = 2%$. The number of non - defective products mis - classified as defective is $99050\times2%=99050\times\frac{2}{100}=1981$. But we are interested in defective products delivered, so we focus on the mis - classified defective ones.
Answer:
19 (closest to 20 among the given options)