yes
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Parametric.
If the distribution is parametric then yes.
Parametric statistical tests assume that your data are normally distributed (follow a classic bell-shaped curve). An example of a parametric statistical test is the Student's t-test.Non-parametric tests make no such assumption. An example of a non-parametric statistical test is the Sign Test.
* Always when the assumptions for the specific test (as there are many parametric tests) are fulfilled. * When you want to say something about a statistical parameter.
A classic would be the Kolmogorov-Smirnov test.