# Math Help - Probabilities involving the sum or difference of independent Normal random variable

1. ## Probabilities involving the sum or difference of independent Normal random variable

Applying torque A machine fastens plastic screw-on caps onto containers of motor oil. If the machineapplies more torque than the cap ean withstand, the capwill break. Both the torque applied and the strength ofthe caps vary. The capping-machine torque T follows aNormal distribution with mean 7 inch-pounds and standard deviation 0.9 inch-pounds. The cap strength C (thetorque 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 cap will break whilebeing fastened by the machine?
b.) Explain why it is reasonable to assume that the capstrength and the torque applied by the machineare independent.