Answer:
Confidence limit = [52.8%, 75.2%]
Step-by-step explanation:
[tex]P=\frac{45}{70}= 0.64[/tex]
[tex](1-P)=1-0.64=0.36[/tex]
[tex]n= 70[/tex]
[tex]P[/tex] ± [tex]z[/tex] [tex]\sqrt{\frac{P(1-P)}{n} }[/tex]
where the value [tex]z[/tex] will be taken from the z-table for 95% confidence interval
1-0.95= 0.05/2= 0.025
0.95+0.025= 0.0975
From the z-table the value of [tex]z[/tex] corresponding to 0.0975 is 1.96
[tex]0.64[/tex] ± [tex]1.96[/tex] [tex]\sqrt{\frac{0.64*0.36}{70} }[/tex]
[tex]0.64[/tex] ± [tex]1.96[/tex] [tex](0.057)[/tex]
[tex]0.64[/tex] ± [tex]0.112[/tex]
[tex]64%[/tex]% ± [tex]11.2[/tex]%
so the confidence interval is
[tex]64+11.2=75.2[/tex]%
[tex]64-11.2=52.8[/tex]%
[tex][52.8, 75.2][/tex]
