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. (Rockwell hardness is measured on a continuous scale.)
(Round the Z value 2-decimal places and the probability to 4-decimal places)
If a specimen is acceptable only its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness.
