A security team is setting up a new walk-through metal detector and decided to run some tests on the current calibration of the machine. Members of the team walk through carrying metallic items of different sizes. Some items are weapons which should cause the alarm to sound. Other items are harmless, like jewelry or coins, which should not cause the alarm to sound. The following table shows the results of their test. (a) Positive (alarm sounds) 127 Negative (no alarm) Totals Weapon True Positive False Negative 11 138 Harmless Item False Positive 246 True Negative 86 332 Answer as a percentage rounded to two decimal places. Show your calculations. 2. What is the probability of a positive test result from the metal detector? Totals 373 97 470 3. What is the probability of a positive test result from the metal detector given that a weapon is present? This is the sensitivity of the metal detector. 4. What is the probability of a negative test result from the metal detector given that a weapon was present? This is the false negative rate of the metal detector. 5. What is the probability of a negative test result from the metal detector given that a harmless item was present? This is the specificity of the metal detector. 6. What is the probability of a positive test result from the metal detector given that a harmless item was present? This is the false positive rate of the metal detector.
A security team is setting up a new walk-through metal detector and decided to run some tests on the current calibration of the machine. Members of the team walk through carrying metallic items of different sizes. Some items are weapons which should cause the alarm to sound. Other items are harmless, like jewelry or coins, which should not cause the alarm to sound. The following table shows the results of their test. (a) Positive (alarm sounds) 127 Negative (no alarm) Totals Weapon True Positive False Negative 11 138 Harmless Item False Positive 246 True Negative 86 332 Answer as a percentage rounded to two decimal places. Show your calculations. 2. What is the probability of a positive test result from the metal detector? Totals 373 97 470 3. What is the probability of a positive test result from the metal detector given that a weapon is present? This is the sensitivity of the metal detector. 4. What is the probability of a negative test result from the metal detector given that a weapon was present? This is the false negative rate of the metal detector. 5. What is the probability of a negative test result from the metal detector given that a harmless item was present? This is the specificity of the metal detector. 6. What is the probability of a positive test result from the metal detector given that a harmless item was present? This is the false positive rate of the metal detector.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A security team is setting up a new walk-through metal detector and decided to run some tests on the current
calibration of the machine. Members of the team walk through carrying metallic items of different sizes. Some
items are weapons which should cause the alarm to sound. Other items are harmless, like jewelry or coins, which
should not cause the alarm to sound. The following table shows the results of their test.
(a)
Positive (alarm sounds)
Negative (no alarm)
Totals
Weapon
True Positive
127
False Negative
11
138
Harmless Item
False Positive
246
True Negative
86
332
Answer as a percentage rounded to two decimal places. Show your calculations.
2. What is the probability of a positive test result from the metal detector?
Totals
373
97
470
3. What is the probability of a positive test result from the metal detector given that a weapon is present?
This is the sensitivity of the metal detector.
4. What is the probability of a negative test result from the metal detector given that a weapon was present?
This is the false negative rate of the metal detector.
5. What is the probability of a negative test result from the metal detector given that a harmless item was
present? This is the specificity of the metal detector.
6. What is the probability of a positive test result from the metal detector given that a harmless item was
present? This is the false positive rate of the metal detector.
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