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.)

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?