Specifications for the shaft of an electric motor indicate the diameter of the shaft must be within 0.5±0.01 inches to be considered non-defective. data from inspectors indicate that currently, shaft diameters follow a normal distribution with mean m=0.505 and standard deviation s=0.005.
a) what fraction of shafts will be defective?
b) suppose the mean shifts to m=0.5, now what fraction of shafts will be defective?
c) suppose the mean stays at m=0.5, and you want to reduce the standard deviation so that 99.9% of the shafts are non-defective. what value of s will produce the desired result?