I don't hold PhD in stats, but i do some of it for leaving (and even published a book on applied algebra problems with some stat examples in it). In my humble opinion the frequentist statistics tells us that percentage of sample to population does not matter as much as the absolute size of the sample. Thus, e.g., even assuming unlimited population (infinite universe-to-sample ratio), binomial test would have approx. 39.8% to 60.2% for 95% error bounds on a 50/50 sample with no replacement. Hundreds of data points is pretty good w.r.t. error bounds.
IMO at this point what matters more is the distortion of assumptions. Namely, the biggest two are stationary distribution assumption (i.e., simply speaking, that production rate doesn't change with time, which it does) and sample bias (we have a power to yank data points from population completely at random accross all parameters, including dates, which we do not). But Tesla has the knowledge to adjust better for these than we do, which is why i am saying i am inclined to trust their estimates even more.
Part of what I was referring to was degrees of freedom /CI. We 'know' there are 420,000 cars reserved/ordered. Some of them are overseas, some are for standard range battery, some are for LR RWD (largely turned to revenue at this point) and the rest are AWD. I believe Tesla said orders were about 50/50 SR to LR or maybe it was RWD to AWD. Where I'm going with this is to simplify 210,000 are US, 105,000 are SR, 50,000 are AWD. Yes there are assumptions and some error injected in that mathematical educated guesswork.
The other interesting thing Troy said, there were several, was he felt initially maybe 9% of actual reservations were self reporting but felt now it was around 2. This implies incomplete data. He also said he removed what he perceived to be bad data, reservations with no invites, invites with no orders. Very old orders with no VIN, VINs with no date or delivery. So, yeah, bad data. If they have 50,000 AWD orders and can crank out 5,000-6,000 per week. Then there is color batching, they may spend a week doing Obsidian Black and the next week doing MCR.
Granted likely all lines aren't doing AWD but I bet the bulk are. So many assumptions are predicated on facts not in evidence. Then there are the inevitable unknown unknowns.
I don't have a PhD in Math, I do have 12 semester hours in statistics and much of my career was spent working with statistical data. And, at the end of the day, VINs will arrive when they arrive. I do feel bad for those who ordered 2 1/2 yrs ago. I ordered a yr ago.
It is my considered opinion those people who ordered March and April of 2016, will be the first to be built. A friend of mine in La Jolla, CA said there are model 3 AWDs all over the place now.