Question

1. (13pts) Steel rods are manufactured with a mean length of 25 centimeters (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.

(a) What proportion of rods have a length of exactly 25.07 cm?

(b) What proportion of rods has a length less than 24.9 cm?

(c) Any rods that are shorter than 24.85 cm or longer than 25.15 cm are discarded. What proportion of rods will be discarded?

(d) Using the results in part (c), if 5,000 rods are manufactured in a day, how many should the plant manager expect to discard?

(e) If an order comes in for 10,000 steel rods, how many rods should the plant manager manufacture if the order states that all rods must be between 24.9 cm and 25.1 cm?

Answer 1