I have often wondered HOW they decide who is invited to the Olympics. Turns out it isn't completely complicated. There are 2 qualifying times, "A" time and "B" time, and the International Athletics Federation tracks people's time different certified meets. Of course, in case with throws it "distance" not "time", but generally you get the idea.
You (as Country X) can send up to 1, 2 or 3 athletes if they all meet the "A" time. If none of Country X's athletes meet the "A:" time, but a few meet the "B" time, you may send any one (1) of those athletes that meets the "B" time. If you are a country that has no athletes that meet either time, you can send a single athlete in each event.
If you want to know what the A and B bars are set at, here they are (from Wikipedia):