I advise strongly against using k-means here. The results for different values of k aren't very well comparable. The method is just a crude heuristic.

Instead, the obvious approach is to try fitting a single Gaussian function and (for example using the Levenberg-Marquard method) fit three Gaussian functions, maybe constrained to the same height (to avoid degeneration).

Then test, which of the two distributions fits better.

I advise strongly against using k-means here. The results for different values of k aren't very well comparable. The method is just a crude heuristic. If you really want to use clustering, use EM clustering, since your data seems to contain normal distributions. And validate your results!

Instead, the obvious approach is to try fitting a single Gaussian function and (for example using the Levenberg-Marquard method) fit three Gaussian functions, maybe constrained to the same height (to avoid degeneration).

Then test, which of the two distributions fits better.