Question

The women’s heptathlon in the Olympics consists of seven track and field events: the 200-m and 800-m runs, 100-m high hurdles, shot put, javelin, high jump, and long jump. In the 2000 Olympics, the best 800-m time, run by Gertrud Bacher of Italy, was 8 seconds faster than the mean. The winning long jump by the Russian Yelena Prokhorova was 60 centimeters longer than the mean. Bacher’s winning 800-m time of 129 seconds was 8 seconds faster than the mean qualifying time of 137 seconds (the standard deviation of the qualifying times was 5 seconds). Prokhorova’s winning long jump was 60cm longer than the average 6-m jump (Note: the standard deviation of the long jumps was 30 cm). Which performance is more outstanding (and hence deserves more points when computing their overall score)? Explain.

Answer 1

Answer: Prokhorova is more outstanding.

Step-by-step explanation: To compare scores from different distributions, first standardize it:

z-score = $\frac{x-\mu}{\sigma}$

where

x is the individual mean you want to compare

μ is the mean of the population

σ is standard deviation

For Gertrud Bacher:

z-score = $\frac{129-137}{5}$

z-score = $-1.6$ (s)

The negative sign indicates Bacher's mean is less than the mean

For Yelena Prokhorova:

z-score = $\frac{660-600}{30}$

z-score = 2 (cm)

The positive sign indicates Prokhorova's mean is more than the mean.

Using z-score table, you determine the percentiles are:

For Bacher: Percentile = 5.5%

For Prokhorova: Percentile = 97.7%

Bacher's percentile means she is above 5.5% of the participants, while Prokhorova is 97.7% above the other competitors, which means Prokhorova have a better performance and deserves more points.