8. In a random sample of 80 components of a certain type, 12 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 probabil ity that a component works properly, how can P(system works) be expressed in terms of p?]

c. Let be the sample proportion of successes. Is an unbiased estimator for p2? Hint: For any rv Y, E(Y2)  V(Y)  [E(Y)]2.