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In Exercises 21鈥24, use these results from the 鈥1-Panel-THC鈥 test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana Use

a. How many subjects are included in the study?

b. How many of the subjects had a true negative result?

c. What is the probability that a randomly selected subject had a true negative result?

Short Answer

Expert verified

a.The number of subjects is equal to 300.

b.The number of subjects who had a true negative result is equal to 154.

c.The probability of selecting a subject who had a true negative result is equal to 0.513.

Step by step solution

01

Given information

The given data shows the number of positive and negative drug test results of subjects.

The values are categorized as true and false results.

02

Define probability

For an event A, the probability of its occurrence is computed as shown below:

PA=NumberofoutcomesresultinginATotalnumberofoutcomes

03

Calculation

The table below shows the number of subjects that fall in each category:


True Result

False Result

Total

Subject Tested Positive

143 鈥 24 =119

24

143

Subject Tested Negative

157 鈥 3 = 154

3

157

Total

273

27

Grand Total=300

a.

The total number of subjects is given as follows:

119+24+154+3=300

Therefore, the total number of subjects is equal to300.

b.

The number of subjects who had a true negative test result is given by:

157-3=154

Therefore, the number of subjects who had a true negative test result is equalto 154.

c.

Theprobability of selecting a subject who had a true negative test result is given as follows:

PTruenegativeresult=NumberofsubjectswhohadatruenegativeresultTotalnumberofsubjects=154300=0.513

Therefore, the probability of selecting a subject who had a true negative test result is equalto 0.513.

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