Jul2. Chapter 7 Review Quiz This Question This Quiz:8pl Steel rods are manufadtu

Question

Jul2. Chapter 7 Review Quiz This Question This Quiz:8pl Steel rods are manufadtured with a mean length ol 20 centimeter (cm) Because of variability in the mandachuaing process, the lenglths of the sods are approximately nomally distributed with a standard deviation of 0.07 cm Complete parts (a) to (d) (a) what proportn otrok has a ling h less han 199 ar? pound to four nal places as teeded ) (bAny rods that aee shorter tuan 1984orlongerthan 2016 are doarded What proporion of rods wil bedi carded? (Round to four decinal places as needed) Using the results ot part(b). 5000 rods are manufactured in a day, how many should the plant manager expect todecard? (Use the answer from part b to ind this answer Round to the nearest integer as needed) (d ilan order comes in for 10,000 steel rods, how many tods should the plant manager expect to manfachure # the order states that all rods must be between 19.9 am and 20 1 cm? Round up to the nearest integer) Enter your answer in each of the answer boxes

Explanation / Answer

a) P(X<19.9)=P(Z<(19.9-20)/0.07)=P(Z<-1.4286)=0.0766

b)

Pproportion =1-(19.84<X<20.16)=1-P(-2.2857<Z<2.2857)=1-(0.9889-0.0111)=1-0.9777 =0.0223

c)

numbers =np=5000*0.0223=~111

d)P(19.9<X<20.1)=P(-1.4286<Z<1.4286)=0.9234-0.0766=0.8469

hence expected number to manufacture =10000/0.8469=11809

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