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. if the acceptable range of hardness is (70 2 c, 70 1 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 indepen-dently 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? [hint: y 5 the number among the ten specimens with hardness less than 73.84 is a binomial variable; what is p? ]