Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
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.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.