Question

In Exercises 21–24, refer to the sample data in Table 4-1, which is included with the Chapter Problem. Assume that 1 of the 555 subjects included in Table 4-1 is randomly selected.

	Positive Test Result (Test shows drug use)	Negative Test Result (Test shows no drug use)
Subject Uses Drugs	45 (True Positive)	5 (False Negative)
Subject Does Not Use drugs	25 (False Positive)	480 (True Negative)

Drug Testing Job Applicants Find the probability of selecting someone who does not use drugs. Does the result appear to be reasonable as an estimate of the proportion of the adult population that does not use drugs?

Short answer

The probability of selecting a person who does not use drugs is 0.90990.

Yes, the value appears to be reasonable for estimating the proportion of adults who do not use drugs.

Step-by-step solution

Given information

A sample of 555 job-seeking candidates are drug tested, and their results are categorized under four headings.

Define probability

Probability measures the possibility of an event.

Mathematically, it is represented as

$P\left(A\right)=\frac{\text{Number}\text{of}\text{outcomes}\text{resulting}\text{in}A}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Calculate the probability 

Let A be the event that the selected person does not use drugs.

Here,the number of people who do not use drugs is the sum of the number of people who tested true negative and false positive.

The total number of persons who got tested is 555.

The probability of event A is

$$\begin{gathered} P\left(A\right)=\frac{Numberofpersonswhodonotusedrugs}{Totalnumberofpersons} \\ =\frac{25+480}{555} \\ =\frac{505}{555} \\ =0.910 \end{gathered}$$

Therefore, the probability of selecting a person who does not use drugs is 0.910.

Discuss if the probability is a reasonable estimate

The computed probability value appears to be a reasonable estimate of the actual proportion of adults who do not use drugs.