In a random sample of 160 components of a certain type, 56 are found to be defec

Question

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.)

Explanation / Answer

solution:-

a.  we want find a point estimate of the proportion of all such components

given that 56 out of 160 components of certain type of defective

160-56 = 104

so 104 of 160 components are not defective we can use this sample ratio of non defective components as a point estimate = 104/160

= 0.65 components are non defective

b. the system is to be constructed by randomly selecting two of these components and connecting is

0.65*0.65 = 0.4225

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