If a probability distribution has, say, 112 bins with around 29000 samples, with the maximum probability of a bin being less than 0.05, is the Jarque-Bera test an effective measure of conformance to a Normal distribution?

I'm working with univariate data, whose probability distribution 'looks' normal, with some deviation. However, the Jarque-Bera test for normality indicates that it is *not* normal.

Also, since n ~ 29000, the JB statistic is inflated to a ridiculous value like 1474523. Am I doing something wrong? Any help would be most welcome.

The Jarque Bera statistics and a histogram for these data are:

```
n = 28535.0
Skewness = -4.24685767755943
Kurtosis = 37.1765663807246
JB statistic = 1474523.40413686

```

![Histogram](https://i.stack.imgur.com/NboDn.png)