I have the following exercise question I am trying to answer: 

If the standard error of the sampling distribution of the sample
proportion is 0.0229 for samples of size 400, then the population
proportion must be either:
0.5 or 0.5.
0.4 or 0.6.
0.3 or 0.7.
0.2 or 0.8.

I am using the "Standard error of the proportion" equation to solve for
the proportion (p) and arrive at an answer close to 0.3 or 0.7.  However I am
not certain that I am actually going about it the right way and that
my answer is actually correct.

I would like to know the best way to solve this.

The formula for the standard error of a sample proportion is
sqrt(p(1-p)/n). So here .0229 = sqrt(p(1-p)/400). This gives p(1-p) =
.210 (approximately). So p = .3 or .7.

Thanks bc. Its good to know I have the right equation.  I also come
out at .210 but I am inclined to rather give an answer of p = .2 or .8
as a result of rounding down to .2