Question

Acme Manufacturing Company requires all of its 4750 employees to take a drug

test. Suppose 4% of the employees actually use drugs (although the company does not know this number). The drug test is 98% accurate.

- How many of Acme’s employees use drugs?
- How many of the employees who use drugs get a positive test result?
- How many of the employees who do not use drugs get a positive test result?
- 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?

- State a conclusion about the accuracy of the test.

Answer #1

Positive Result | Negative | Total | |

Use Drugs | 186.2 | 3.8 | 190 |

Not Use Drugs | 91.2 | 4468.8 | 4560 |

Total | 277.4 | 4472.6 | 4750 |

1)

Here Total Employee = 4750

Employee who use drugs = 4750 *0.04 = **190**

2)

Since test is 98% accurate

Positive among this will be = 0.98 * 190 **=
186.2**

3)

employees who do not use drugs = 4750 -190 = 4560

get a positive test result = 4560 *0.02 =
**91.2**

4)

employees who get a positive test result, how many of them use

drugs = **186.2 (from the table above)**

5)

percent of people who get a positive result actually use drugs =
186.2 / 277.4 = **67.12%**

**Please revert back in case of any
doubt.**

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