Question

5. Suppose a large shipment of compact discs contained 12% defectives.

If a sample of size 457 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%? Round your answer to four decimal places.

6.The mean cost of a five pound bag of shrimp is 46 dollars with a standard deviation of 7 dollars.

If a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would differ from the true mean by less than  0.5 dollars? Round your answer to four decimal places.

Answer 1

5)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.1200
sample size       =n=	457
std error of proportion=σp=√(p*(1-p)/n)=	0.01520

probability =

P(0.09<X<0.15)

=

P(-1.97<Z<1.97)=

0.9756-0.0244=

0.9512

6)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	46
std deviation   =σ=	7
sample size       =n=	49
std error=σx̅=σ/√n=	1.0000

probability =

P(45.5<X<46.5)

=

P(-0.5<Z<0.5)=

0.6915-0.3085=

0.3830