Please help!

Steel rods are manufactured with a mean length of 24 centimeters (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 23,9 cm?

(Round to four decimal places as needed) - The answer I got was a z-score of 0.1335

(b) Any rods that are shorter than 23.78 cm or longer than 24.22 cm are discarded. What proportion of rods will be discarded?

(Round to four decimal places as needed.)

(c) Using the results of part (b). Of 5000 rods are manufactured in a day, how many should the plant manager expect to discard?

5000 * ?

(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 23.9 cm and 24.1 cm.

How do I solve (b) - (d)? I use formula X-U/standard deviation. However, my answers do not match the practice quizzes.