Problem #3 : Suppose that 21% of all steel shafts produced by a certain process

Question

Problem #3 : Suppose that 21% of all steel shafts produced by a certain process are nonconforming but can be reworked (rther than having to be scrapped) (a) In a random sample of 165 shafts, find the approximate probability that between 20 and 47 (inclusive) are nonconforming and can be reworked (b) In a random sample of 165 shafts, find the approximate probability that at least 36 are nonconforming and can be reworked Problem #3(a): Problem #3(b) Just Save Submit Problem #3 for Grading Problem #3 | Attempt #1 | Attempt #2 | Attempt #3 3(a) 3 (b) 3(a) 3(b) Your Answer: 3(a) 3(b) Your Mark: 3(a) 3 (b 3(a) 3(b 3(a)

Explanation / Answer

here proporion of nonconfoming=p=0.21 and we use standard normal variate z=(x-mean)/sd

(a) sample size=n=165, mean=np=165*0.21=34.65

and standard deviation=sd=sqrt(np(1-p)=sqrt(165*0.21*(1-0.21))=5.23

for x=20, z=(20-34.65)/5.23=-2.8012

for x=47,  z=(47-34.65)/5.23=2.3614

P(20<=x<=47)=P(-2.8012<z<2.3614)=P(z<2.3614)-P(z<-2.8012)=0.9909-0.0025=0.9884

(3b) P(at least 36 are nonconforming ...)=P(X>=36)=P(Z>0.2581)=1-P(Z<0.2581)=1-0.6018=0.3982

for X=36, z=(36-34.65)/5.23=0.2581

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