Answer
Sampling distribution of p̂ is normally distributed with $μ_{p̂} = 0.7$ and $σ_{p̂} = 0.026$
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) = 300 x 0.7 x 0.3 = 63 $\geq 10$
Hence sampling distribution of p̂ is normally distributed.
$μ_{p̂} = p = 0.7$
$σ_{p̂} = \sqrt \frac{p(1-p)}{n}$
$ = \sqrt \frac{0.7 * 0.3}{300}$
= 0.026
