We are asked to determine the p-values for a proportion that is greater than 0.51. Since we are asked about the hypothesis being greater then the p-value is given by:
[tex]p-\text{value}=P(z>3.065)[/tex]
This is a right-tailed test. To determine this probability we need to use the fact that:
[tex]P(z>3.065)=P(z<-3.065)[/tex]
replacing we get:
[tex]p-\text{value}=P(z<-3.065)[/tex]
Now, from the tables for z-scores in the normal distribution we get:
[tex]p-\text{value}=0.0011[/tex]
Therefore, the p-value is 0.0011
