A machine fastens plastic screw-on caps onto containers of motor oil. If the mac

Question

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 has the normal distribution with mean 6.9 inch-pounds and standard deviation 0.99 inch-pounds. The cap strength (the torque that would break the cap) has the normal distribution with mean 10.4 inch-pounds and standard deviation 1.3 inch-pounds.

(b) What is the probability that a cap will break while being fastened by the capping machine?

Explanation / Answer

B) This requires the torque of the capping machine, C has normal dist with mean 6.9, s.d. 0.99.
The cap strength S has normal dist with mean 10.4, s.d. 1.3
The cap will break if C>S or C-S>0 and you require P(C-S>0).
Mean of C-S =6.9-10.4=-3.5 and s.d (C-S), since C and S are independent =sqrt(0.99^2+1.3^2) =1.6. P(C-S>0)= P(z> (0- -3.5)/1.6)=P(Z>2.1875)=0.0144

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