Steel rods are manufactured with a mean length of 29 centimeter (cm). Because of

Question

Steel rods are manufactured with a mean length of 29 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. Complete parts (a) to (d)

(a) What proportion of rods has a length less than 28.9 cm?

(b) Any rods that are shorter than 28.84 cm or longer than 29.16 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?

(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

28.9 cm and 29.1 cm?

Explanation / Answer

a) Get the z-score: z=(x-)/, where =mean and =standard deviation..

z=(28.9-29)/0.07 = -1.42857
Using Excel (or you can use a calculator or table), P(Z<z) = P(Z<-1.42857) = 7.6564%

b) Since both lengths are exactly 0.15 away from the average, we just need to do one side and then double the result.
z=(28.84-29)/0.07 = -2.185

P(Z<z) = P(Z<-2.14286) = 1.1135%
so double it for a 2-tail result: 2*1.1135% = 2.227%

c) 2.227%*5000 = 111.35, or about 111 rods discarded

Please post part d saperately. Hope this above will be helpful to you. Thanks and God bless you :-)

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