Questions: Question 16, 4.2.21 HW Score: 76.47%, 13 of 17 Part 1 of 3 points (*) Points: 0 of 1 Save Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 24 false positive results. Among 154 negative results, there are 4 false negative results. Complete parts (a) through (c). (Hint: Construct a table.) a. How many subjects were included in the study? The total number of subjects in the study was

Question 16, 4.2.21 HW Score: 76.47%, 13 of 17 Part 1 of 3 points (*) Points: 0 of 1 Save Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 24 false positive results. Among 154 negative results, there are 4 false negative results. Complete parts (a) through (c). (Hint: Construct a table.) a. How many subjects were included in the study? The total number of subjects in the study was
Transcript text: Question 16, 4.2.21 HW Score: $76.47 \%, 13$ of 17 Part 1 of 3 points (*) Points: 0 of 1 Save Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 24 false positive results. Among 154 negative results, there are 4 false negative results. Complete parts (a) through (c). (Hint: Construct a table.) a. How many subjects were included in the study? The total number of subjects in the study was $\square$
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Solution

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Solution Steps

Step 1: Calculate the Total Number of Subjects

Using the formula $Total\ Subjects = TPR + TNR$, we find the total number of subjects by adding the total positive results (145) and the total negative results (154). $$Total\ Subjects = 145 + 154 = 299$$

Step 2: Calculate the Number of True Negative Results

Using the formula $True\ Negative\ Results = TNR - FNR$, we find the number of true negative results by subtracting the false negative results (4) from the total negative results (154). $$True\ Negative\ Results = 154 - 4 = 150$$

Step 3: Calculate the Number of Subjects Who Did Not Use the Substance

The number of subjects who did not use the substance is equivalent to the number of true negative results, which is 150.

Step 4: Calculate the Probability That a Randomly Selected Subject Did Not Use the Substance

Using the formula $Probability = \frac{Subjects\ Who\ Did\ Not\ Use}{Total\ Subjects}$, we find the probability by dividing the number of subjects who did not use the substance (150) by the total number of subjects (299). $$Probability = \frac{150}{299} = 0.5$$

Final Answer:

The probability that a randomly selected subject did not use the substance is approximately 0.5.

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