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Suppose that 23% of all steel shafts produced by a certain process are nonconforming but can...

Suppose that 23% 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 222 shafts, find the approximate probability that between 45 and 64 (inclusive) are nonconforming and can be reworked.
(b) In a random sample of 222 shafts, find the approximate probability that at least 55 are nonconforming and can be reworked.

Please do not round up the numbers during the process, as I am on my last try.

I have tried 0.8143for part a and 0.2643 for part b.

Math   Statistics-And-Probability   
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