Suppose 62% of batteries obtained from a major supplier last beyond warranty period. A random sample of 33 batteries is selected.

Assuming independence, use the binomial formula or software (recommended) to answer the following questions. Report probabilities accurate to at least 4 decimal places. What is the probability that, of the 33 batteries selected: a) exactly 20 last beyond warranty period? b) exactly 11 do not last beyond warranty period? c) all of them last beyond warranty period? d) no less than 18 last beyond warranty period? e) no more than 20 last beyond warranty period? f) at least 18 and at most 20 last beyond warranty period? g) more than half last beyond warranty period?