But in scientific and mathematical use, “normal” means anything that you can reasonably expect to recur. It may be common or uncommon. It may be within one standard deviation of the mean, or further out, but if you can state a probability of its occurrence, then it is normal. It’s something that happens often enough to measure.
So, cancer is normal. That doesn’t mean that I can state with confidence that you will get cancer, or any particular kind of cancer, but I can look up the odds on it, adjusting for genetics and lifestyle as necessary. Mental illness is normal; that is, a certain percentage of people will have condition X, and you can state that probability with some confidence. Crime is normal; we don’t pass laws against things we don’t think will ever happen. The crime rate rises and falls, so you can affect crime; but no one has ever managed to eliminate it so we hire policemen. Broken hearts are normal. And not just bad things are “normal” – winning the lottery is a thing that happens (though not, probably to you), and you can predict the odds, so that’s normal, too.
In terms of sexual behavior, there is no kind of behavior that we are seeing today that has not been practiced throughout history. Even the Vikings had words in Old Norse for things they swore were never practiced by them. But then, why have the words? The words testify to the existence of the acts, however rare. In this sense, everything we see today is “normal.”
But normal doesn’t mean okay. It doesn’t establish the goodness of anything. “Whatever IS, is RIGHT” is from Alexander Pope’s poem, Essay on Man. He appeals to Nature as the standard of morality. But Nature includes (see above), cancer, mental illness, crime, and broken hearts. Are those felt as right and good when we experience them? Far from it.
So, where does the definition of “good” come from? Ah, now you’re asking something. And we can talk about that. But first, let’s dispose of the idea that the mere exhibition of something – and the acceptance of that something by society – makes “normal” into “good.” It does no such thing.