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Suppose the past data indicates that the probability of a fluorescent light produced from a production line has a useful life of at least 800 hours is 0.95. Batches that consist of 24 fluorescent lights from this production line are checked for its useful life. Let X be the number of fluorescent light that do not have a useful life of at least 800 hours.
(a) What is the probability that there are anywhere from 2 to 4 (inclusive) that do not have a useful life of at least 800 hours in a batch?
(b) What is the probability that there are at least 20 fluorescent lights having a useful life of at least 800 hours in a batch?
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