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
1)
for normal distribution z score =(p̂-p)/σ_{p} | |
here population proportion= p= | 0.0700 |
sample size =n= | 247 |
std error of proportion=σ_{p}=√(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=σ_{p}=√(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=σ_{p}=√(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 |
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