Answer:
(a) 0.85
(b) 0.7225
Step-by-step explanation:
(a) The point estimate for the proportion of all such components that are not defective is given by the number of non-defective units in the sample divided by the sample size:
[tex]p=\frac{80-12}{80}\\p=0.85[/tex]
The proportion is 0.85.
(b) Assuming that the sample is large enough to accurately provide a point estimate for the whole population, this can be treated as a binomial model with probability of success (non-defective part) p = 0.85. Since both components must be non-defective for the system to work, the probability of two successes in two trials is:
[tex]P(x=2) = 0.85^2\\P(x=2) = 0.7225[/tex]
An estimate of 0.7225 for the proportion of all such systems that will function properly.