A city commissioner claims that 80% of the people living in the city favour contracting out garbage collection to a private company. To test the commissioner's claim, 25 city residents are randomly selected, yielding 22 who prefer contracting to a private company. (a) If the commissioner's claim is correct, what is the probability that the sample would contain at least 22 who prefer contracting to a private company? (b) If the commissioner's claim is correct, what is the probability that exactly 22 would prefer contracting to a private company? (c) If 100 city residents are randomly selected, how many would you expect to prefer contracting to a private company.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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: A city commissioner claims that 80% of the people living in the city favour contracting out
garbage collection to a private company. To test the commissioner's claim, 25 city residents are randomly
selected, yielding 22 who prefer contracting to a private company.
(a)  If the commissioner's claim is correct, what is the probability that the sample would contain at
least 22 who prefer contracting to a private company?
(b)  If the commissioner's claim is correct, what is the probability that exactly 22 would prefer
contracting to a private company?
(c)  If 100 city residents are randomly selected, how many would you expect to prefer contracting
to a private company. 

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