Ball bearings are manufactured with a mean diameter if 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed, with a standard deviation of 0.02 mm.

a) What proportion of ball bearings has a diameter more than 5.03 mm?
b) Any ball bearings that have diameter less than 4.95 mm or greater than 5.05 mm are discarded. What proportion of ball bearings will be discarded?
C) Using the results of part (b), if 30,000 ball bearings are manufactured in a day, how many should the plant manager except to discard?
D) Determine the 25th percentile for the diameter of the ball bearings
E) Determine the interquartile range of the diameters of the ball bearings