Answer :
To determine which statement is supported by the data, we need to analyze the false positive rate based on the given data. Here is a step-by-step solution:
1. Number of Computers Tested:
Total number of computers tested:
[tex]\[ \text{Total computers} = 500 \][/tex]
2. Number of Infected and Not Infected Computers:
- Number of computers infected with the virus:
[tex]\[ 28 + 12 = 40 \][/tex]
- Number of computers not infected with the virus:
[tex]\[ 94 + 366 = 460 \][/tex]
3. False Positives:
These are computers which the program reported as infected, but they were actually not infected. From the table:
[tex]\[ \text{False positives} = 94 \][/tex]
4. False Positive Rate Calculation:
The false positive rate is calculated as the number of false positives divided by the total number of non-infected computers, multiplied by 100 to convert it to a percentage:
[tex]\[ \text{False positive rate} = \left(\frac{\text{False positives}}{\text{Number of not infected}}\right) \times 100 \][/tex]
So, substitute the values we have:
[tex]\[ \text{False positive rate} = \left(\frac{94}{460}\right) \times 100 \approx 20.43\% \][/tex]
Conclusion:
The calculated false positive rate is approximately [tex]\(20.43\%\)[/tex].
Based on the provided statements:
- Statement D matches the calculated false positive rate statement, but with a small difference in percentage (22.95% instead of 20.43%).
Therefore, none of the statements perfectly matches the specific calculated false positive rate of [tex]\(20.43\%\)[/tex]. However, if we are to choose the closest one among the provided options, we'd say:
D. The magazine's review suggests Nate should use a different detection program because the probability that the scan false positive is [tex]\(22.95\%\)[/tex].
This choice is closest to the actual false positive rate calculated from the given data.
1. Number of Computers Tested:
Total number of computers tested:
[tex]\[ \text{Total computers} = 500 \][/tex]
2. Number of Infected and Not Infected Computers:
- Number of computers infected with the virus:
[tex]\[ 28 + 12 = 40 \][/tex]
- Number of computers not infected with the virus:
[tex]\[ 94 + 366 = 460 \][/tex]
3. False Positives:
These are computers which the program reported as infected, but they were actually not infected. From the table:
[tex]\[ \text{False positives} = 94 \][/tex]
4. False Positive Rate Calculation:
The false positive rate is calculated as the number of false positives divided by the total number of non-infected computers, multiplied by 100 to convert it to a percentage:
[tex]\[ \text{False positive rate} = \left(\frac{\text{False positives}}{\text{Number of not infected}}\right) \times 100 \][/tex]
So, substitute the values we have:
[tex]\[ \text{False positive rate} = \left(\frac{94}{460}\right) \times 100 \approx 20.43\% \][/tex]
Conclusion:
The calculated false positive rate is approximately [tex]\(20.43\%\)[/tex].
Based on the provided statements:
- Statement D matches the calculated false positive rate statement, but with a small difference in percentage (22.95% instead of 20.43%).
Therefore, none of the statements perfectly matches the specific calculated false positive rate of [tex]\(20.43\%\)[/tex]. However, if we are to choose the closest one among the provided options, we'd say:
D. The magazine's review suggests Nate should use a different detection program because the probability that the scan false positive is [tex]\(22.95\%\)[/tex].
This choice is closest to the actual false positive rate calculated from the given data.
