Question: Applying torque A machine fastens plastic screw-on caps onto containers of motor oil. If the machine applies more torque than the cap can withstand, the cap will break. Both the torque applied and the strength of the caps vary. The capping-machine torque T follows a Normal distribution with mean 7 inch-pounds and standard deviation 0.9 inch-pounds. The cap strength C (the torque that would break the cap) follows a Normal distribution with mean 10 inch-pounds and standard deviation 1.2 inch-pounds.
(a) What is the probability that a randomly selected cap has a strength greater than 11 inch-pounds?
(b) Explain why it is reasonable to assume that the cap strength and the torque applied by the machine are independent.
(c) Let the random variable D = C - T. Find its mean and standard deviation.
(d) What is the probability that a randomly selected cap will break while being fastened by the machine? Show your work.