Steel rods are manufactured with a mean length of 30 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.07 cm. Complete parts (a) to (d). (a) What proportion of rods has a length less than 29.9 cm? (Round to four decimal places as needed.) (b) Any rods that are shorter than 29.83 cm or longer than 30.17 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 states that all rods must be between 29.9 cm and 30.1 cm? (Round up to the nearest integer.)