Question

Steel rods are manufactured with a mean length of 2828 centimeter​ (cm). Because of variability in the manufacturing​ process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.09cm.

.​(a) What proportion of rods has a length less than 27.9​cm?

​(Round to four decimal places as​ needed.)

​(b) Any rods that are shorter than 27.78 cm or longer than 28.22 cm are discarded. What proportion of rods will be​ discarded?

​(Round to four decimal places as​ needed.)​

(c) Using the results of part​ (b), 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 27.9 cm and

28.1 ​cm?

​(Round up to the nearest​ integer.)

Answer 1