Normal Random Variables: Plotting CDF/Variance

So I'm trying to get an edge on Discrete Math for next fall, and I'm working on this problem:

Suppose that X is a normal random variable with mean 3. If P{X > 4} = 0.1, what is the variance of X? What should be c such that P{X < c} = 0.2? Plot the PDF of this r.v., then plot its CDF.

would the Variance just be:

$Var(X) = (4 - 3)^2*.1 = (4-3)*.1 = 1 * .1 = .1$?

Also, how do I compute the p.d.f. for a normal random variable? Is it just:

P(X) = $(1 / (\sqrt(2 * (\pi) * (\sigma ^ 2)))$ * e ^$-((x - (\mu))^2$/$2*(\sigma ^2))$

I think I'm doing something very wrong, but I can't figure out what.

Thank you.