Answer
Sampling distribution of p̂ is approximately normal, with $μ_{p̂} = 0.4$ and $σ_{p̂} = 0.22$
Work Step by Step
5% of population = 25,000 x 0.05 = 1,250, hence sample size is less than 5% of population.
np(1-p) = 500 x 0.4 (0.6) = $120 \geq 10$
Hence sampling distribution of p̂ is approximately normal.
$μ_{p̂} = p = 0.4 $
$σ_{p̂} = \sqrt\frac{ p(1-p)}{n}$
$= \sqrt\frac{ 0.4(0.6)}{500}$
= 0.022
