The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of
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. If the acceptable range of hardness is (70 - c, 70 + c), for what value of c would 95% of all specimens have acceptable hardness?
c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?
d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than 73.84?
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