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Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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In a random sample of 160 components of a certain type, 56 are found to be defective.
(a) Give a point estimate of the proportion of all such components that are not defective.
(b) A system is to be constructed by randomly selecting two of these components and connecting them in series, as shown here.
The series connection implies that the system will function if and only if neither component is defective (i.e., both components work properly).
Estimate the proportion of all such systems that work properly. [Hint: If p denotes the probability that a component works properly, how can
P(system works) be expressed in terms of p?] (Enter your answer to four decimal places.)
Transcribed Image Text:In a random sample of 160 components of a certain type, 56 are found to be defective. (a) Give a point estimate of the proportion of all such components that are not defective. (b) A system is to be constructed by randomly selecting two of these components and connecting them in series, as shown here. The series connection implies that the system will function if and only if neither component is defective (i.e., both components work properly). Estimate the proportion of all such systems that work properly. [Hint: If p denotes the probability that a component works properly, how can P(system works) be expressed in terms of p?] (Enter your answer to four decimal places.)
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