Question

Steel rods are manufactured with a mean length of 23 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.

(a) What proportion of rods has a length less than 22.9 cm?

(b) Any rods that are shorter than22.83 cm or longer than 23.17 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? 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 22.9 cm and 23.1 cm? (Round up to the nearest​ integer.)

Answer 1

Hello Sir/ Mam

Given that:

Mean =	23.00
Standard Deviation =	0.07

(a)

(b)

Hence,

1.52% of the rods will be discarderd.

(c)

No. of rods to be discarded = 5000*1.52% = 75.79 approximately equal to 76 rods.

(d)

Hence,

No. of rods to be manufactured = 10000/84.69% = 11808 rods

I hope this solves your doubt.

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