Answer
Sampling distribution of p̂ is normally distributed with $μ_{p̂} = 0.42$ and $σ_{p̂} = 0.013$
Work Step by Step
5% population size = 1,500,000 x 0.05 = 75,000, hence sample size is less than 5% population size.
np(1-p) = 1460 x 0.42 x 0.58 = 355.656 $\geq 10$
Hence sampling distribution of p̂ is normally distributed.
$μ_{p̂} = p = 0.42$
$σ_{p̂} = \sqrt \frac{p(1-p)}{n}$
$ = \sqrt \frac{0.42 * 0.58}{1460}$
= 0.013
