Suppose that 27% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). (a) In a random sample of 227 shafts, find the approximate probability that between 53 and 67 (inclusive) are nonconforming and can be reworked. (b) In a random sample of 227 shafts, find the approximate probability that at least 65 are nonconforming and can be reworked.

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