When a small percentage is presented as a normality

It depends on what is meant by 'normal'. If X is said to be so, this could mean "X is statistically in the majority" (1), "X is statistically common" (2), or "there is nothing untoward about X" (3).

Example: 
5000 apples
4800 of those apples are red
200 of the apples are green
Therefore green apples are normal.

This is an example of (3), I believe. While green apples are a tiny minority in this sample of 5000, there is of course, nothing wrong with green apples.

But, if they were trying to imply (1) or (2), I'd say that'd be factually inaccurate.

Here's an example of (2). The prevalence of allergic rhinitis in the U.S. is between 15-30%, which, although not in the 'majority', is still somewhat frequent. It wouldn't be unusual for you to run into someone with the condition.

An example of (1) would be heterosexuality.

Besides the comment below from Rationalissimus of the Elenchus, you are assuming the green apples are somehow not "perfect" or normal. There are varieties of apples that are green and never become any other color.  Presented as you have, it looks more like an inventory than a logical question. You might want to rewrite the question. 

One of the fallacies could be hasty generalization. For example, suppose that we have a box with 5000 apples, 200 of them are green. John doesn't know how many apples there are in the box. He picks up 4 at random, sees that all of them are green and concludes that it is normal to pick up green apples. 

I think it is important to note though that the words "normal" and "tiny" might be loaded. On the one hand, "normal" seems to suggest that things are large enough. On the other, "tiny" seems to suggest that things are not that normal. 

Normal (common) but tiny.

Example 1: Suppose that 1 out of 20 people believe that the earth is flat. Out of a group of 200 people, only 10 believe that the earth is flat. This is a tiny number but normal (common).

Normal and large enough.

Example 2: If we have a larger group from example 1, say 20,000 people, then 1,000 believe that the earth is flat. Here, it is common for people to believe that the earth is flat and the number is large enough.

Not normal (likely to be chosen) and tiny

Example 3: That'll be your apples example if we assume equal likelihood for picking an apple at random.

Normal (likely to be chosen) and tiny

Example 4: All apples are in a box and all the green ones are placed on top. It is normal to pick up a green apple even if the number is tiny.