The first time I saw the issue was also on my day one iPhone 5, but it wasnt as bad as on my 2nd iPhone 5S. Actually I dont believe that there are generally some serial numbers the faulty ones, but i believe there is always some bunch of serial numbers affected since they were produced together. I also think that these phones which got produced together will go in a big box together and will be delivered to the same retail place together (for example in my local Apple Store all displayed slate and white 5S have an F2 serial number and all gold ones have DN, I dont think thats just coincidence). Therefore it is very possible that one store has 95% affected phones while another maybe has 0%.
I still believe that one of the three supplier makes inferior panels which cause the black lines etc. So in theory the chances to get a faulty panel is 1 to 3. The thing we dont know is if all three suppliers really produce ⅓ of the iphone displays. Therefore the affected phones could be more or less than ⅓.
And I still recommand, if you dont see any black lines during normal usage (or have anything else that bothers you about the display) then dont even try out the test image. This thread isnt about convincing people that their good phones are faulty.

It's about helping people who see the issue and are looking for advice how to get a replacement that isnt affected.