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 2,000 20 950
Answer
Answer:
20
Explanation:
Step1: Calculate actual defective products
The number of manufactured products is $n = 100000$, and the defect - rate is $0.95%=0.0095$. So the number of actual defective products is $100000\times0.0095 = 950$.
Step2: Calculate non - detected defective products
The test is $98%$ accurate at determining if a video game is defective. So the non - detection rate of defective products is $(1 - 0.98)=0.02$. The number of defective products that pass the test (and will be delivered) is $950\times0.02=19$.
Step3: Calculate false - positive non - defective products
The number of non - defective products is $100000\times(1 - 0.0095)=100000\times0.9905 = 99050$. The false - positive rate (non - defective products wrongly identified as defective) is also $(1 - 0.98)=0.02$. The number of non - defective products wrongly identified as defective is $99050\times0.02\approx1981$. But we are interested in defective products delivered, so we focus on non - detected defectives. Rounding $19$ to the nearest option, we get 20.