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Normal approximation to a binomial distribution

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Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be re-worked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming, what is the (approximate) probability that X is:

a. At most 30
b. Less than 30
c. Between 15 and 25 (inclusive).

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This solution uses a normal approximation to a binomial distribution to answer the given probability questions.

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