In an earlier example, you read how Simone Biles won the gold medal in women's artistic gymnastics at the 2016 Olympics. Her overall score in this event was 62.366. Her overall score in this event was 62.366. Forty years earlier, Romanian Nadia Comaneci took the world by storm with the first perfect 10. With an overall score of 79.275, Comaneci also won the all-around gold medal. Because the scoring systems have changed, these two scores aren't directly comparable.

1. In 2016, the 24 gymnasts in the all-around had a mean score of 57.261 points with a standard deviation of 1.565 points. Calculate and interpret the z-score for SImone Biles' scores in 2016.
2. In 1976, the 24 gymnasts in the all-around had a mean score of 76.527 points with a standard deviation of 1.327 points. Calculate and interpret the z-score for Nadia Comaneci's score in 1976.
3. Based on your answers to parts a and b, which gymnast has a better performance? Explain your reasoning.