While the original distribution is clearly non-normal, the sample size is so large that the distribution of the mean will be approximately normal:
(that's the distribution of the sample mean for 10000 samples of the same size as your sample from the empirical cdf. Which is to say, it's the bootstrap distribution of the sample mean).
Further, the distribution of the standard error of the mean is pretty tight, so that you could reasonably treat the null distribution as normal with $\sigma = s$. So you could do a z-test.
Or you could base a test directly off the bootstrap distribution above; it suggests a very small p-value.