Answered: the swab results are normally…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.
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?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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