Integrated circuits from a certain factory pass a certain quality test with probability 0.8. The outcomes of all tests are mutually independent.
(a) What is the expected number of tests necessary to find 500 acceptable circuits?
(b) Use the central limit theorem to estimate the probability of finding 500 acceptable circuits in a batch of 600 circuits.
(c) Use Matlab to calculate the actual probability of finding 500 acceptable circuits in a batch of 600 circuits.
(d) Use the central limit theorem to calculate the minimum batch size for finding 500 acceptable circuits with probability 0.9 or greater.