Answer
Sampling distribution of p̂ is normally distributed with $μ_{p̂} = 0.8$ and $σ_{p̂} = 0.046$
Work Step by Step
5% population size = 10,000 x 0.05 = 500, hence sample size is less than 5% population size.
np(1-p) = 75 x 0.8 x 0.2 = 12 $\geq 10$
Hence sampling distribution of p̂ is normally distributed.
$μ_{p̂} = p = 0.8$
$σ_{p̂} = \sqrt \frac{p(1-p)}{n}$
$ = \sqrt \frac{0.8 * 0.2}{75}$
= 0.046
