When to expect when you are expecting

They were expecting their third child – a daughter – a week after Labor Day. Perfect timing: their older kids will be out of the house and back to school, and the doctors back in town. All was well except that a few months before he realized that the September 12th due date fell inconveniently close to a professional conference in Europe, which he organized. “To go or not to go?” was pulsating daily in his brain. Will she manage here with 2.5 kids on her 9th month of pregnancy without me? What are her chances of delivering 3 weeks earlier? Shall I bring my mother to help here instead of me? If I stay – something will surely be messed up at the conference. Who will do my part? What would my colleagues say about me abandoning them? It is an honorable responsibility and I want to see it through.

***

Due date is calculated based on the empirical observations that it takes an average of 38 weeks from the moment of conception to the moment of delivery. But no one knows when exactly conception took place and how fast the sperm moved and fertilized the egg, plus it may be embarrassing to admit that you did it while at your in-laws or on a friend’s couch. So we look around for the closest related landmark – the menstrual period. Its first day usually is 10-18 days before the conception. So, your due date is approximately:
38 weeks + [10-18] before conception days =roughly 40 weeks from the first day of your last menstrual period
And ironically enough, when you conceive you are already considered 2 weeks pregnant.

The actual birth dates are spread around this 40 week due date in approximately normal distribution (bell curve).

(Graph from Ref 1.)
Graph mark of 24% at the 40th week mean that your chances of delivering on any day of this week are approximately 24%/7=3.4%. You can see that around 90% of babies are born within three weeks of their due date, and 21% are born within 3 days of it. In many geographical places, the right side of this distribution is sharply raised and cut at 42 weeks because the majority of the women that have not delivered by the 42nd week are being induced.

Why does the gestational age vary? Because not everyone ovulates and conceives exactly 14 days after the beginning of the menstrual period; some babies mature faster while some are too comfy inside; second and further babies seems to be more in a rush to come out; mother’s age and weather may influence the dates; and women of some ethnicities tend to give birth a bit earlier than others. (Ref 2, 3, 4)

Back to our expecting couple. He took from Wikipedia the data about probability distribution of actual births with respect to their due date.



He centered the graph on their due date, September 12th. Total area under this bell curve is equal to 1 = accumulated probability of giving birth. The chances of delivery during any interval are equal to the area under this interval. He marked in red the probability of her delivering prior to August 27th while he is away. He added up all the red area under the curve obtaining 0.043. He proudly showed it to her, explaining that her chances of giving birth before he returns are only 4.3%.
She told that this may be true but he is a 100% asshole. She also reminded him that both of their older kids were born two weeks earlier.
He still went abroad and run the conference.
She gave birth a week and a half after his return (on September 8th) to a healthy and beautiful baby girl.
They lived happily ever after, but he was never forgiven.


References:

1. Calculating Due Dates and the Impact of Mistaken Estimates of Gestational Age
2. Gestational Age at Birth, 1994 and 2004
3. American Pregnancy Association
4. Duration of human singleton pregnancy. A population-based study.