Question

A manufacturing process produces 5.5% defective items. What is the probability that in a sample of 51 items:

a. 11% or more will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Probability            

b. less than 1% will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Probability            

c. more than 11% or less than 1% will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Probability            

Answer 1

here population proportion=     μp=	0.0550
sample size       =n=	51
std error of proportion=σp=√(p*(1-p)/n)=	0.0319

a)

probability =P(X>0.11)=P(Z>(0.11-0.055)/0.032)=P(Z>1.72)=1-P(Z<1.72)=1-0.9573=0.0427

b)

probability =P(X<0.01)=(Z<(0.01-0.055)/0.032)=P(Z<-1.41)=0.0793

c)

probability =1-P(0.01<X<0.11)=1-P((0.01-0.055)/0.032)<Z<(0.11-0.055)/0.032)=1-P(-1.41<Z<1.72)=1-(0.9573-0.0793)=0.1220