How do we know, we are having a normal distribution?

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I am not a mathematician, I always had problem understanding this and perhaps someone can help me.

Let's assume, we have collected data of students height. If our sample is big enough, we know we will have normal distribution.

But my question is: Is there a mathematical way, where we can set an input of the data and find out what distribution we are facing?

What if we do not know, our data is about students height. What if it would be a uniform distributed data... Taking mean and std of this data, could be quiet useless for further investigation.

So is there a way, to at least check if the data we are having has normal distribution or not. And if it is: Could you explain it to me. Thank you