Steel rods are manufactured with a mean length of 20 cerdmeter (cm), Because of

Question

Steel rods are manufactured with a mean length of 20 cerdmeter (cm), Because of variablity n the normally distributed with a standard deviation of 0.05 cm process, the lengths of the rods are approximately Click the icon to view a table of areas under the normal curve (a) What proportion of rods has a length less than 19.9 cm? (Round to four decimal places as needed.) is s (b) Any rods that are shorter than 19.88 cm or longer than 20.12 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 rds must be between 19 9 cm and 20.1 cm? (Round up to the nearest integer) Enter your answer in each of the answer boxes

Explanation / Answer

a|)

b)

therefore proportion of defective =1-P(19.88<X<20.12) =1-0.9836 =0.0164

c)

expected to be discarded =np =5000*0.0164 =82

d)

hence to be manuactured =10000/0.9545 =~ 10477

for normal distribution z score =(X-)/ here mean=       = 20.000 std deviation   == 0.0500

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