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Steel rods are manufactured with a mean length of 28 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.08 cm Click the icon to view a table of areas under the normal curve (a) What proportion of rods has a length less than 27.9 cm? (Round to four decimal places as needed.) (b) Arry rods that are shorter than 27.81 cm or longer than 28, 19 cm are discarded. What proportion of rods will be discarded? (Round to four decimal places as needed.) (c) Using the results of part (b), if 5000 rods are manufactured in a day. how many should the plant manager expect to discard? (Use the answer from part b to find this answer, Round to the nearest integer as needed.) (d) If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order slates that all rods must be between 27.9 cm and 28,1 cm? (Round up to the nearest integer.)