How to choose a distribution for the likelihood step?

I think you can just do this?

non_centered = az.load_arviz_data('non_centered_eight')
az.plot_density(non_centered.posterior, var_names=["mu"])

or

non_centered = az.load_arviz_data('non_centered_eight')
az.plot_posterior(non_centered.posterior, var_names=["mu"])

There is no sigma parameter.