Answer
$ μ_{p̂} = p = 0.82$
$σ_{p̂} = 0.038$
Work Step by Step
Here we have: n = 200, p = 0.82
Verifying model requirements:
a. np(1-p) = 100 x 0.82 (1 - 0.82) = 14.76
b. n is less than 5% of about 300+ million US citizens.
Hence, p̂ is normally distributed.
$ μ_{p̂} = p = 0.82$
$σ_{p̂} = \sqrt \frac{p(1-p)}{n} = \sqrt \frac{0.82(1-0.82)}{100} = 0.038$
