Question

1. Suppose a large shipment of telephones contained 7% defectives. If a sample of size 247 is selected, what is the probability that the sample proportion will be greater than 9%? Round your answer to four decimal places

2. Suppose 48% of the population has myopia. If a random sample of size 484 is selected, what is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3%? Round your answer to four decimal places

3. A film distribution manager calculates that 9% of the films released are flops. If the manager is correct, what is the probability that the proportion of flops in a sample of 835 released films would be greater than 7%? Round your answer to four decimal places

Answer 1

1)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.0700
sample size       =n=	247
std error of proportion=σp=√(p*(1-p)/n)=	0.0162

probability =P(X>0.09)=P(Z>(0.09-0.07)/0.016)=P(Z>1.23)=1-P(Z<1.23)=1-0.8907=0.1093

2)

std error of proportion=σp=√(p*(1-p)/n)=

0.0227

probability =P(0.45<X<0.51)=P((0.45-0.48)/0.023)<Z<(0.51-0.48)/0.023)=P(-1.32<Z<1.32)=0.9066-0.0934=0.8132

3)

std error of proportion=σp=√(p*(1-p)/n)=

0.0099

probability =P(X>0.07)=P(Z>(0.07-0.09)/0.01)=P(Z>-2.02)=1-P(Z<-2.02)=1-0.0217=0.9783