11 August 2008

Lucky babies redux

Two babies born at 8:08 am on 8/8/08, weighing eight pounds, eight ounces, both in the United States.

How many would you expect?

The 2007 crude birth rate for the US is 14.2 per 1000, per year; the estimated US population is 304,843,316. The product of these is 4,328,775 births per year, or 8.25 births per minute.

From here I can find the distribution of birth weights (in Norway, 1992-1998 -- better figures would be appreciated). About six percent of babies weigh between 3850 and 3950 grams, which is a 3.5-ounce-wide interval; thus about 6%/3.5 = 1.7% of babies weigh 8 pounds, 8 ounces (to the nearest ounce) at birth.

So the expected number of babies born in the US at that particular minute, at that weight, is about 1.7% of 8.25, or 0.14.

There were two. The probability of this happening, assuming births are a Poisson process, is about one in 112. I wouldn't trust this number too much, because birth weights are supposedly growing with time and the Norwegian distribution is probably different from the US distribution.

So if I had to guess, people at the hospitals are fudging the numbers; if we were being totally honest, those babies might turn out to have been born at 8:09 am and weighed eight pounds, seven ounces, or something like that. Not that there's anything wrong with that.

(This post borrows a lot from a post I just remembered I made, lucky babies, about babies born on July 7, 2007 at 7:07 and weighing seven pounds, seven ounces -- but those were fictional babies.)


Chris Wellons said...

Don't we sort-of want to look at it as the chance of something "interesting" occurring with dates and births rather than some specific event (a bunch of eights)? The chances of this will be much higher.

For example, a friend and I once walked into a typical tabletop gaming/comic book store and found a 100-sided die. Fascinated, as neither of us had seen one before, he picked it up, rolled it, and got a 100 on the first roll.

"Wow! What are the chances of that?" he said before thinking, which was funny to us at the time because it seemed so well defined (1 in 100 chance of walking in and rolling a 100 right away).

But what we are *really* looking at is the probability of walking in and rolling something interesting. This would probably include both 1 and 100, and maybe even 50. Suddenly the event doesn't seem as improbable as we first thought (1 in 50, or 1 in 33).

Anonymous said...

Hmmm, I had an 8-pound, 8 oz baby .... but in February 2005. Does she get any luck for that?

Anonymous said...

No reporting on 08/08/08 at 8 lbs. even? Just leaving out the ounces leaves us with all those 8's... and 8 is much more likely than 8 and a half...