A machine manufactures parts whose diameters vary according to the normal distribution with the mean = 40.150 mm and the standard distribution is 0.003 mm. An inspector randomly selects four parts manufactured by this machine and finds the average diameter of 40.148 mm.
a) Within what limits should the middle 99% of the individial parts be?
b) Within what limits does the middle 99% of the sampling distribution for samples of size 4 fall?