In a random sample of 80 components of a certain type, 20 are found to be defect

Question

In a random sample of 80 components of a certain type, 20 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

a)

no of components that are not defective = 80-20 =60

point estimate of the proportion of all such components that are not defective = 60/80 = 6/8 = 3/4 = 0.75

b)

since both the components work independent of each other probabity that both components work is P(first component is not defective)*P(second component is not defective)

P(system works) = probabity that both components work = P(first component is not defective)P(second component is not defective)

P(first component is not defective) = P(second component is not defective) = 0.75

probability that a component works properly = 0.75*0.75 = 0.5625

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