The TSA randomly swabs carryon bags to test for traces of explosives. After swabbing the luggage with a specially coated pad, it is inserted into a chemical analyzer which determines the level of certain compounds. If the test comes back positive, the passenger is subject to additional screening steps, otherwise they are free to continue on. For bags that do contain prohibited explosive chemicals, the swab results are normally distributed with a mean of 10 and a standard deviation of 3. For bags that do not contain prohibited explosive chemicals, the swab result is normally distributed with a mean of 7 and a standard deviation of 4. The TSA sets the threshold of 8 – i.e. if the swab result is ≥ 8, the test is considered positive.
The TSA randomly swabs carryon bags to test for traces of explosives. After
swabbing the luggage with a specially coated pad, it is inserted into a chemical analyzer which
determines the level of certain compounds. If the test comes back positive, the passenger is
subject to additional screening steps, otherwise they are free to continue on. For bags that do
contain prohibited explosive chemicals, the swab results are
of 10 and a standard deviation of 3. For bags that do not contain prohibited explosive
chemicals, the swab result is normally distributed with a mean of 7 and a standard deviation
of 4. The TSA sets the threshold of 8 – i.e. if the swab result is ≥ 8, the test is considered
positive.
**** PLEASE DO D AND E***
a. What percentage of bags with explosives will be correctly identified using this cutoff?
b. What percentage of bags which do not have explosive material will also be mistakenly
identified as positive due to this cutoff?
c. What percentage of bags with explosives will slip through this swab test?
d. Recompute the answers to (a), (b), (c) if the TSA increases the threshold to 9?
e. In less than 100 words discuss what factors you would consider in setting an
appropriate threshold value for the swab test.
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