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First of all, the support of a normal distribution is the entire real line (or, in general, $\mathbb{R}^n$ for an $n$-dimensional multivariate normal distribution) so your action can be any number in $\mathbb{R}$. What you may be getting confused with is that with probability 0.68 you will obtain an action that is within +/- 1 standard deviation from the ...

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