Let $Z \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is a gaussian random real number with parameters $\mu \in \mathbb{R}$ and $\sigma \in [0, \infty)$ if and only if $$\begin{equation} X \overset{d}{=} \sigma Z + \mu \end{equation}$$