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Mailrooms contaminated with anthrax. During autumn 2001,
Chapter 4, Problem 31E(choose chapter or problem)
Mailrooms contaminated with anthrax. During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mailrooms for the presence of anthrax spores. Let x equal the number of mailrooms contaminated with anthrax spores in a random sample of n mailrooms selected from a population of N mailrooms. The researchers showed that the probability distribution for x is given by the formula
\(p(x)=\frac{\left(\begin{array}{l}k \\ x \end{array}\right)\left(\begin{array}{l} N-k \\ n-x \end{array}\right)}{\left(\begin{array}{c} N \\ n \end{array}\right)}\)
where k is the number of contaminated mailrooms in the population. (In section 4.4 we identify this probability distribution as the hypergeometric distribution.) Suppose N = 100, n = 3, and k = 20.
a. Find p(0).
b. Find p(1).
c. Find p(2).
d. Find p(3).
Questions & Answers
QUESTION:
Mailrooms contaminated with anthrax. During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mailrooms for the presence of anthrax spores. Let x equal the number of mailrooms contaminated with anthrax spores in a random sample of n mailrooms selected from a population of N mailrooms. The researchers showed that the probability distribution for x is given by the formula
\(p(x)=\frac{\left(\begin{array}{l}k \\ x \end{array}\right)\left(\begin{array}{l} N-k \\ n-x \end{array}\right)}{\left(\begin{array}{c} N \\ n \end{array}\right)}\)
where k is the number of contaminated mailrooms in the population. (In section 4.4 we identify this probability distribution as the hypergeometric distribution.) Suppose N = 100, n = 3, and k = 20.
a. Find p(0).
b. Find p(1).
c. Find p(2).
d. Find p(3).
ANSWER:Step 1 of 5
The experiment under consideration here is sampling of mailrooms for the presence of anthrax spores.
A sample of n mailrooms from a population of N mailrooms is selected which contains x number of mailrooms contaminated with anthrax spores.
The researchers showed that x has the probability distribution
p(x)=
where k is the number of contaminated mailrooms in the population.
Also, it is given that N=100, n=3 and k=20.
Using this we need to find the required values.