# Normal approximation to a binomial distribution

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).

See the attached file.

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#### Solution Summary

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

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