I've been wondering what the distribution of babys' births are
relative to their Estimated Due Date (EDD). For example how many babies
are born before 37th week (pre-term), at the start of the 37th week,
end of 37th week, start of 38th week etc. up to after 42nd week.
Ideally it would be some study with a daily granularity so I can see
the cumulative chance of when a baby is likely to arrive by a certain
date!

I understand that first babies are normally later, so there may well
be different statistics for first and subsequent babies. I also found
out that 10% are born after the 42nd week and 5% born on due date, but
I'm looking for a greater level of detail than that. I would have
thought that somewhere Out There is some study with what surely should
be common knowledge in midwifery circles. A quick google myself didn't
find anything though.

Thanks.

Dear jifl2-ga,

Thanks for the opportunity to address this interesting question!  As I
had two "late" deliveries myself, I had previously done some research
on the subject.

First of all, there is a question of how to determine a due date. 
There are several different methods and all of them can return
different results.  Occasionally the results can be inaccurate, since
many women do not ovulate on the 14th day of their cycle.  In fact,
there was even a recent study done that shows some women ovulate
multiple times during one menstrual cycle:

-Yahoo News - Women May Ovulate More Than Once a Month: Study
http://story.news.yahoo.com/news?tmpl=story&u=/nm/20030708/wl_canada_nm/canada_health_ovulation_col_1

Although this study has not yet been independently verified, the
implications could be fairly important in the ob/gyn sphere.

So how does one determine a due date?  The method most people are
familiar with is called Naegele’s Rule.  Add 280 days to the date of
the last menstrual period, or 266 days to the date of ovulation, if
known.  This was an arbitrary rule developed by Franz Naegele in 1812
according to his belief that pregnancies _should_ last ten lunar
months.

Secondly is Mittendorf's formula, based on his observation that most
first time, or primaparous, women gave birth 8 days later than the due
date calculated by Naegele's Rule.  Women who had given birth before,
or multiparous women, on average gave birth 3 days past their Naegele
due date.  Black women tended to give birth 8.5 days earlier than
white women.  Therefore, the Mittendorf formula is:

(LMP – 3 months) + 15* Days = Due Date
* Add 10, rather than 15, if mother is non-white, or multiparous

-PubMed: The Length of Uncomplicated Human Gestation
http://www.ncbi.nlm.nih.gov:80/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2342739

-Calculating Due Dates
http://www.transitiontoparenthood.com/ttp/birthed/duedatespaper.htm

According to a German doctor in the early 1800s, there is even a
formula for determining gestation length in the Talmud:  "The regular
pregnancy from the day of fertilization until the delivery has a
duration of 270 days or 9 months, each month counted as 30 days."

-Due Date (Frank Peinemann)
http://frank.peinemann.bei.t-online.de/medicine/duedate.htm

As you can see, there is no one definitive way to tell when a baby is
due.  Some babies just need to "bake" longer, and some are perfectly
happy coming out sooner.  Each method can vary the due date by days,
and therefore skew the delivery statistics that you are interested in.

Now to the meat of the matter. You want to know the distribution of
babies that are born full-term during the 37th, 38th, 39th, etc.
weeks.  Unfortunately there is nothing out there with raw data per day
- everything seems to be compiled per week.  Most all information I
have seen follows the pattern of a bell chart with the peak around 40
weeks, so you can safely assume that the highest percentage numbers
given up until 40 weeks are for the _end_ of the week, and after 40
weeks are for the _beginning_ of the week.  Understandably this
involves some smoothing, but from my research I have seen no
large-scale multinational studies done, so undoubtedly the figures you
get will be close but not exact.

"I have found multiple references that state that about 6% of babies
are pre-term, and that 4-14% of babies would be born after 42 weeks
(Odutayo, and others), if it were not for interventions..."

-Calculating Due Dates, ibid.

The Calculating Due Dates (
http://www.transitiontoparenthood.com/ttp/birthed/duedatespaper.htm )
page also has a graph with percentages broken down per week, from
extrapolated data from different sources.  It states that births break
down as follows (from eyeballing the bar graph):
 
Before 37 weeks: 4%
37 weeks: 5%
38-39 weeks: 10%
39-40 weeks: 20%
40-41 weeks: 35%
41-42 weeks: 20%
Over 42 weeks: 10%

(the numbers do not add up to 100%, but unfortunately data is not
given for the graph)

The page also gives a distribution of data from births in Alaska from
1990-1998, and notes that there may be a racial difference in the
Alaskan study because "Native infants on average weigh slightly more
than non-Native infants".

Very preterm babies, under 33 weeks, were 1.9%.  
Preterm babies, 33-36 weeks, were 9.4%.  
Term babies, 37-41 weeks, were 81.6%.  
Postterm babies, 42 weeks and over, were 9.0%

A midwife states:

"I have just finished our 1995 stats (I know, I know....I'm a little
slow, but I do all the data and we had 479 women (with 487 babies...6
sets of twins, 2 sets of triplets) that year. 217 primips...

Of these 479 women: 

140 (29.2%) delivered between 40-41 weeks 
105 (21.9%) delivered between 41-42 weeks 
27 (5.6%) delivered between 42-43 weeks 
1 went >43 completed weeks"

-Gentlebirth Postdates archive
http://gentlebirth.org/archives/postdates.html

There is a Canadian study contrasting gestational age at birth between
1972 and 1986 here:

-eCMAJ -- Joseph and Kramer 161 (11):1409
http://www.cmaj.ca/cgi/content/full/161/11/1409

with a line graph of percentage of live births vs. gestational age in
weeks here:
http://www.cmaj.ca/cgi/content/full/161/11/1409/F129

Another Canadian study of term births is available here:

-Recent Trends in Fetal and Infant Outcomes Following Post-term
Pregnancies
http://www.hc-sc.gc.ca/pphb-dgspsp/publicat/cdic-mcc/22-1/a_e.html

with the following breakdowns:

1985-1987
37 weeks - 4.76%
38 weeks - 12.65%
39 weeks - 19.54%
40 weeks - 37.27%
41 weeks - 13.71%
42 weeks - 4.96%
43+ weeks - 0.41%

1992-1993
37 weeks - 5.69%
38 weeks - 14.36%
39 weeks - 21.56%
40 weeks - 32.44%
41 weeks - 14.65%
42 weeks - 3.40%
43+ weeks - 0.13%

I assume the missing percentage applies to births before 37 weeks.

It is interesting to note that due dates are normally the beginning of
the 40th week.  According to these studies, you only have a 29-37%
chance of delivering in your 40th week!

I hope this answer suits your needs, and I thank you heartily for
giving me the opportunity to research something so interesting!  If
you have any other questions or concerns, please use the Clarification
Request feature so that I may help further.

Search strategy used:
Henci Goer's book, The Thinking Woman's Guide to a Better Childbirth,
makes note of the discrepancy in calculating due dates and the
inclination for induction by the medical community for post-term
babies.  This provided me with a starting point for my search.  She
related the Mittendorf study in the appendix.

Google searches:
"length of uncomplicated human gestation"
"estimated due date statistics"
"gestational age distribution"
"distribution percentage human gestation weeks"

A brilliant answer. I feel like I can't give the full 5 because there
there isn't the granularity I was after, but it seems that if there is
any study out on the web it all, it may not be google-able.
Nevertheless the answer was very complete, thank you!

I asked this same question a while back:
http://answers.google.com/answers/main?cmd=threadview&id=110577

At that time, the consensus was that there was no scientific answer.
Anyway, my results was that she came 1 day early.