Answer: 0.0895
Step-by-step explanation:
Let p= population proportion.
Given : Sample size : n= 500
p= 0.47
Required probability = [tex]P(\ha{p}>0.50)[/tex]
[tex]=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.50-0.47}{\sqrt{\dfrac{0.47(1-0.47)}{500}}}) \\\\=P(z>1.344)\ \ \ [z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=1-P(z<1.344)\\\\=1-0.9105\approx0.0895[/tex]
Hence, required probability = 0.0895
