The true average breaking strength of ceramic insulators of a certain type is supposed to be at

Question:

The true average breaking strength of ceramic insulators of a certain type is supposed to be at least 10 psi. They will be used for a particular application unless sample data indicates conclusively that this specification has not been met. A test of hypotheses using α = .01 is to be based on a random sample of ten insulators. Assume that the breaking-strength is normal with unknown standard deviation.
a. If the true standard deviation is .80, how likely is it that insulators will be judged satisfactory when true average breaking strength is actually only 9.5? Only 9.0?
b. What sample size would be necessary to have a 75% chance of detecting that the true average breaking strength is 9.5 when the true standard deviation is .80?
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