(Rockwell hardness is measured on a contin- uous scale.)

a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a ran- domly 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 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 inde- pendently selected specimens have a hardness of less than 73.84? [Hint: Y = the number among the ten specimens with hardness less than 73.84 is a binomial variable; what p?] is