Central Limit Theorem
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The Central Limit Theorem states that as you increase your sample size, your sampling distribution will become normal, no matter if your population distribution is normal or not!
The below visual is from Statistics How To.
It shows how even though the population distribution ("(a) One die") is completely flat (a.k.a. "uniform"), as we increase our sample size (going from (a) ➡️ (e)), our sampling distribution becomes more and more normal!
As we increase our sample size, the means / proportions of those samples will be more consistently closer to the underlying population mean / proportion... and eventually will form a normal distribution around it!
Great! Your sampling distribution will automatically be normal.
When working with proportions, your population distribution cannot be normal. (It's a yes/no value!)
The Central Limit Theorem becomes very helpful here, because our sampling distributions will become normal once we reach a threshold sample size! (See "assumptions")
We must lean on the assumptions for sample means / proportions for this.