Drug Testing

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AcmeManufacturing Company requires all of its 5000 employees to take adrug test. Suppose 2% of the employees actually use drugs (althoughthe company does not know this number). The drug test is 95%accurate.&nbspHowmany of Acme`s employees use drugs? Howmany of the employees who use drugs get a positive test result?Howmany of the employees who do not use drugs get a positive testresult?Ofthe employees who get a positive test result, how many of them usedrugs? Convert this to a percentage: What percent of people who get apositive result actually use drugsStatea conclusion about the accuracy of the test.&nbsp

  1. 5000*0.02=100 employees use drugs.

  2. 100*0.95=95 employees who use drugs get a positive test result.

  3. 5000-100=4900 employees who do not use drugs. 4900*0.05=245 employees who do not use drugs get a positive test result.

  4. 245+95=340 employees get a positive test result (who use and do not use drugs). 95*100/340=27.94% percent of people who get a positive result actually use drugs.

Atfirst look, it seems that results must be good because test has 95%accuracy but, actually, resulst not so good we could think. In ourcase almost 28% of people who get a positive result actually usedrugs. That is meant that 3 of 4 people failed test by not their ownfault.

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