A machine produces bolts in a length (in inches) found to obey a normal probability law with parameters m = 10 and σ = 0.10. The specifications for the bolt call for items with a length (in inches) equal to 10.05 ± 0.12. A bolt not meeting these specifications is called defective.
(i) What is the probability that a bolt produced by this machine will be defective?
(ii) If the machine were adjusted so that the length of bolts produced by it is normally distributed with parameters m = 10.10 and a = 0.10, what is the probability that a bolt produced by the machine will be defective?
(iii) If the machine is adjusted so that the lengths of bolts produced by it are normally distributed with parameters m = 10.05 and σ = 0.06, what is the probability a bolt produced by the machine will be defective?