Answer :
Answer:
[tex] z=\frac{0.07-0.08}{0.00943}= -1.06[/tex]
And we can use the normal standard distribution table and the cmplement rule and we got:
[tex] P(z>-1.06) = 1- P(z<-1.06) = 1-0.1446= 0.8554[/tex]
Step-by-step explanation:
For this case we know the following info given:
[tex]p=0.08[/tex] represent the population proportion
[tex] n= 827[/tex] represent the sample size selected
We want to find the following proportion:
[tex]P(\hat p>0.07)[/tex]
For this case we can use the normal approximation since we have the following conditions:
i) np = 827*0.08 = 66.16>10
ii) n(1-p) = 827*(1-0.08) =760.84>10
The distribution for the sample proportion would be given by:
[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex]\mu_{\hat p}= 0.08[/tex]
And the deviation:
[tex]\sigma_{\hat p}= \sqrt{\frac{0.08*(1-0.08)}{827}}= 0.00943[/tex]
We can use the z score formula given by:
[tex] z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And replacing we got:
[tex] z=\frac{0.07-0.08}{0.00943}= -1.06[/tex]
And we can use the normal standard distribution table and the cmplement rule and we got:
[tex] P(z>-1.06) = 1- P(z<-1.06) = 1-0.1446= 0.8554[/tex]