Answer
$n=336$
Work Step by Step
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$z_{\frac{α}{2}}=z_{0.025}$
If the area of the standard normal curve to the right of $z_{0.025}$ is 0.025, then the area of the standard normal curve to the left of $z_{0.025}$ is $1−0.025=0.975$
According to Table V, the z-score which gives the closest value to 0.975 is 1.96.
Now, the sample size:
$E=0.03$ (within 3 percentage points)
$p̂ =0.086$ (item (a))
$z_{\frac{α}{2}}=z_{0.025}=1.96$
$n=p̂ (1−p̂ )(\frac{z_{\frac{α}{2}}}{E})^2$
$n=0.086(1-0.086)(\frac{1.96}{0.03})^2$
$n=335.52$
Round up:
$n=336$
