Answer
Sampling distribution of p̂ is normally distributed with $μ_{p̂} = 0.65$ and $σ_{p̂} = 0.034$
Work Step by Step
5% population size = 25,000 x 0.05 = 1,250, hence sample size is less than 5% population size.
np(1-p) = 200 x 0.65 x 0.35 = 45.5 $\geq 10$
Hence sampling distribution of p̂ is normally distributed.
$μ_{p̂} = p = 0.65$
$σ_{p̂} = \sqrt \frac{p(1-p)}{n}$
$ = \sqrt \frac{0.65 * 0.35}{200}$
= 0.034
