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 the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (a) If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness? (b) What is the probability that a randomly chosen specimen has a hardness over 80? (c) If the acceptable range of hardness is (70c,70+c), for what value of cc would 95% of all specimens have acceptable hardness