Weddings vs. Births

Our baby is due June 13th. June 13th is right in the middle of wedding season. In fact, I am DJ'ing many weddings near the due date including: May 25, June 1, June 8, June 15, and June 22. May 25th is today, and Shelley is shopping,  so labor seems unlikely (but not impossible). That leaves four weddings that could potentially overlap with Shelley's labor. The worse case scenario is if Shelley goes into labor on a Friday night or Saturday morning before a wedding. I was curious of the probability of this happening and since school is out and I already miss Statistics, I investigated it.

Births relative to due dates are approximately normally distributed with a standard deviation of 10 days. Using excel, I found which dates correlated to the day before and the day of a wedding and converted these intervals to z-scores.

	x	z
26-May-13	-18	-1.8
27-May-13	-17	-1.7
28-May-13	-16	-1.6
29-May-13	-15	-1.5
30-May-13	-14	-1.4
31-May-13	-13	-1.3
1-Jun-13	-12	-1.2
2-Jun-13	-11	-1.1
3-Jun-13	-10	-1
4-Jun-13	-9	-0.9
5-Jun-13	-8	-0.8
6-Jun-13	-7	-0.7
7-Jun-13	-6	-0.6
8-Jun-13	-5	-0.5
9-Jun-13	-4	-0.4
10-Jun-13	-3	-0.3
11-Jun-13	-2	-0.2
12-Jun-13	-1	-0.1
13-Jun-13	0	0
14-Jun-13	1	0.1
15-Jun-13	2	0.2
16-Jun-13	3	0.3
17-Jun-13	4	0.4
18-Jun-13	5	0.5
19-Jun-13	6	0.6
20-Jun-13	7	0.7
21-Jun-13	8	0.8
22-Jun-13	9	0.9

Next, using R, I graphed the probability density function. The area under the entire curve is 1 and the the sum of the shaded regions corresponds to the probability the birth will happen during the intervals that correspond with the weddings.

Using R again, I calculated these probabilities.
> pnorm(-1.2,mean=0,sd=1)-pnorm(-1.3,mean=0,sd=1)
[1] 0.01826919
> pnorm(-.5,mean=0,sd=1)-pnorm(-.6,mean=0,sd=1)
[1] 0.03428442
> pnorm(.3,mean=0,sd=1)-pnorm(.2,mean=0,sd=1)
[1] 0.03865171
> pnorm(.9,mean=0,sd=1)-pnorm(.8,mean=0,sd=1)
[1] 0.02779527

It appears there is an approximately, 11.9% chance the baby will be born while I am working a wedding. This probability represents an uncommon but not rare event, but it is a conservative estimate. DJ'ing a wedding is really about an on-site 8 hour commitment and the probability calculates for a 48 hour interval for each wedding. This means there is less than a 11.9% chance the baby will be born while I am working a wedding. Additionally, even if the 11.9% is accurate, there is an 88.1% chance the baby will not be born during a wedding.