Answer
See below.
Work Step by Step
$x$ has a normal distribution, so the sampling distribution of the sample mean $\overline{x}$ is also normal. The sampling distribution of the sample mean has a mean $\mu=0$ and a standard deviation of $\sigma_{\overline{x}}=\frac{\sigma}{\sqrt n}=\frac{1}{\sqrt{10}}\approx0.316$
