$$0.1=\Pr(X>4) = \Pr\left(\frac{X-\text{mean}}{\text{standard deviation}} > \frac{4-\text{mean}}{\text{standard deviation}}\right)$$$$= \Pr\left(\frac{X-3}{\sigma} >\frac{4-3}{\sigma}\right) = \Pr\left(Z>\frac 1 \sigma\right).$$
So go to the table (or the software that you use) to find the value of $z_0$ such that $0.1=\Pr(Z>z_0)$. Set $1/\sigma = \text{that value}$. That gives you the standard deviation $\sigma$.
The pdf is$$\frac{1}{\sqrt{2\pi}\,\sigma} e^{-((x-\mu)/\sigma)^2/2}.$$