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The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose that the hardness of a particular alloy is normally distributed with a mean of 70 and standard deviation of 3 a) Consider the case where the specimen is only acceptable for hardness between 65 hardness? what range about the mean gives a probability of 95%? The range should be at is the probability that a randomly chosen specimen has an acceptable b) symmetric about the mean.

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