Saturday, March 12, 2011

Calculating a Z Score for Usain Bolt's 100m Time, 2008 Olympic 100m Finals

Here, we are going to calculate a z score for Usain Bolt's time in the finals of the 100m at the 2008 Olympic Games. His z score will be calculated in comparison to his elite peers in that race. In the photo, above, you can see the distance between Bolt and his peers as he crosses the finish line. Here are the athletes' times for the race:
  • Usain Bolt: 9.69 (seconds)
  • Richard Thompson: 9.89
  • Walter Dix: 9.91
  • Churandy Martina: 9.93
  • Asafa Powell: 9.95
  • Michael Frater: 9.97
  • Marc Burns: 10.01
  • Darvis Patton: 10.03
Here, you can watch Bolt blow away the competition in video:

Now in the video, below, we go through process of getting Bolt's z score and then locating it within the standard normal table to check for statistical significance. In the video, we will see that Bolt's time, relative to his peers is statistically significant at the threshold of 0.05. What about at 0.01?

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