Steel rods are manufactured with a mean length of 21 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.09 cm. Complete parts (a) to (d).
(a) What proportion of rods has a length less than 20.9 cm?
(b) Any rods that are shorter than 20.81 cm or longer than 21.19 cm are discarded. What proportion of rods will be discarded?
(c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard?
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