Consider a particular genetic disease affects 3% of adults in the U.S. population. Fortunately, there is a genetic test for the gene that causes the disease. The test is 98% accurate; that is, 98% of the people who take the test get the correct result (and 2% of people tested get the wrong result).
In Springfield, there are 100,000 adults, and they all get tested for the disease.
1 How many of the residents of Springfield are likely to have the disease?
2 How many of the people who actually have the disease get a positive test result?
3 How many of the people who do not have the disease get a positive test result?
4 Of the people who get a positive test result, how many of them have the disease? Convert this to a percentage: What percent of people who get a positive result actually have the disease?
5 What does this percentage tell you about the test?
The problem you must solve is:
1 Acme Manufacturing Company requires all of its 5000 employees to take a drug test. Suppose 2% of the employees actually use drugs (although the company does not know this number). The drug test is 95% accurate.
1 How many of Acme's employees use drugs?
2 How many of the employees who use drugs get a positive test result?
3 How many of the employees who do not use drugs get a positive test result?
4 Of the employees who get a positive test result, how many of them use drugs? Convert this to a percentage: What percent of people who get a positive result actually use drugs?
5 State a conclusion about the accuracy of the test.
To get full credit for this write-up, you should:
1 Answer all parts of the problem.
2 Show your justification for every step in your solution. Use clear, mathematically accurate language.
3 Label all numbers with the units they represent (e.g., 0.3048 ft/meter).
4 Clearly state your conclusions using complete English sentences (for example, "Jill needs to add 43 gallons of water to her pool").