Answered: The TSA randomly swabs carryon bags to…

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 9 – 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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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