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 a mean of 68 and a standard deviation of 3. (Round your answers to 4 decimal places, if needed.) [Note: When needed, correct answers use the provided z-table on eClass, but Excel can also be appropriately used to simulate the table.] (a) If a specimen is acceptable only if its hardness is between 64 and 72, what is the probability that a randomly chosen specimen has an acceptable hardness? (b) If the acceptable range of hardness is (68 c, 68 c), for what value of c would 90% of all specimens have acceptable hardness? (c) If the acceptable range is as in part (a) and the hardness of each of 10 randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the 10? (d) What is the probability that at most 8 of 10 independently selected specimens have a hardness of less than 71.32