From: Julie Jones Laskay [mailto:firstname.lastname@example.org] Sent: Monday, November 14, 2011 10:24 AM To: AP Statistics Subject: [ap-stat] Fun Binomial Example
I just wanted to share with y'all a fun binomial example that illustrates some interesting points.
At the beginning of NFL games, a coin is flipped to determine which team will decide if they will receive the ball to start the 1st or 2nd half. The number of coin flips that a team wins can be modeled with a binomial distribution where p = 0.5 and n = number of games. It's pretty easy for me to convince myself that the flips are independent.
I live in New Orleans, and of course, we love our 2009 World Champion New Orleans Saints.
This year, the Saints have played in 10 regular season games, and they have lost EVERY coin toss. The probability of that happening is (10 C 0)*(.5^0)(.5^10)= 1/1024 = .0009765625.
I think that this is a great example because it shows a couple points: -Even if something is unlikely to happen, it doesn't preclude it from happening. -In statistics, we use data to make conclusions. If something has a .0009765625 chance of happening, we would conclude that if it happens, then something suspicious is going on. However, there is no allegation that the NFL is trying to get the Saints to lose the coin toss. After all, what point would it serve?
As a follow-up, the Saints had a second coin flip yesterday at the start of the overtime period. They lost that coin flip too.
On a personal note, I have really enjoyed using this example because it is a fun way to start Monday morning AP Statistics class. It has really helped my students understand the binomial distribution and appreciate its importance.