Part 1: Metal Detectors

The metal detector at the entrance of a courthouse is used to detect the presence of a weapon when someone enters the building. The metal detector should only sound, indicating a positive test result, when a weapon is present. A metal detector should remain silent, indicating a negative test result, when a weapon is not present.

1. Classify each of the following scenarios as a true positive, false positive, true negative, or false negative. (4 x 2 pt = 8 pt
   1. A person walks through the metal detector and an alarm sounds. This person did not have a weapon.

1. A person walks through the metal detector and the alarm did not sound. The person did not have a weapon.

1. A person walks through the metal detector and an alarm sounds. A weapon was found on the person.

1. A person walks through the metal detector and the alarm did not sound. A weapon was found on the person.

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)	Weapon	Harmless Item	Totals
Positive (alarm sounds)	True Positive _____134_________	False Positive _____260_________	______394________
Negative (no alarm)	False Negative _____11_________	True Negative _____80_________	_____91_________
Totals	______145________	_____340_________	______485________

Answer as a percentage rounded to two decimal places. Show your calculations.

1. What is the probability of a positive test result from the metal detector? (4 pts)

1. 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 pts)

1. 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. (4 pts)

1. 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. (4 pts)

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