Let us define \(G = \ln S\). With \(Ito\) lemma, we have
\[dG = (\mu - \frac{\sigma^2}{2}) dt + \sigma dz,\]
using
\[\frac{\partial G}{\partial S} = \frac{1}{S},
\frac{\partial^2 G}{\partial S^2} = -\frac{1}{S^2},
\frac{\partial G}{\partial t} = 0.\]
Thus
\[\ln S_T - \ln S_0 \sim \phi [(\mu-\frac{\sigma^2}{2})T, \sigma^2 T].\]
where \(S_T\) is the stock price at a future time \(T\), \(S_0\) is the stock price at time 0. In other words, \(S_T\) has a lognormal distribution, which can take any value between 0 and \(+\infty\).