Question

7. Suppose a large shipment of laser printers contained 22% defectives.

If a sample of size 276 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 6%? Round your answer to four decimal places.

10. A film distribution manager calculates that 9% of the films released are flops.

If the manager is right, what is the probability that the proportion of flops in a sample of 435 released films would differ from the population proportion by greater than 4%? Round your answer to four decimal places.

Answer 1

7)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.220
sample size       =n=	276
std error of proportion=σp=√(p*(1-p)/n)=	0.0249

  probability that the sample proportion will differ from the population proportion by less than 6%:

probability =

P(0.16<X<0.28)

=

P(-2.41<Z<2.41)=

0.9920-0.0080=

0.9840

10)

here population proportion=     p=	0.090
sample size       =n=	435
std error of proportion=σp=√(p*(1-p)/n)=	0.0137

  probability that the proportion of flops in a sample of 435 released films would differ from the population proportion by greater than 4%:

P(X>0.13)+P(X<0.05)=1-P(0.05<X<0.13)=1-P(-2.92<Z<2.92)=1-(0.9982-0.0018)=0.0036