Saul and Ricardo are both on the track team but compete in different events. Saul competes in the 200m sprint, and Ricardo competes in the 3000m long-distance run.

At the most recent meet:
- Saul finished his sprint in 22.8 seconds.
- Ricardo finished his race in 11.8 minutes.

The average race times and standard deviations are as follows:
- 200m sprint: average time of 23.4 seconds with a standard deviation of 0.5 seconds.
- 3000m long-distance run: average time of 12.4 minutes with a standard deviation of 0.9 minutes.

Saul believes that his time is better than Ricardo's. Is Saul correct?

Using Z-scores, which quantify how a value deviates from the mean, we find that Saul's score is 1.2 standard deviations below the average, while Ricardo's is only 0.67 below. Thus, in statistical terms, Saul's time is better.

Explanation:

To solve this problem, we need to convert both the 200m sprint and the 3000m long-distance run times into Z-scores. Z-score is something statisticians use to quantify how much an individual value in a dataset deviates from the mean. A Z-score of 0 signifies that the value is exactly average, one of +1 represents a value one standard deviation above the mean, and so on. We can calculate this using the formula: Z = (X - μ) / σ, where X is the value we want to convert, μ is the mean of the dataset, and σ is the standard deviation.

For Saul, we substitute the values into the formula: Z = (22.8 - 23.4) / 0.5 = -1.2. Saul's score is 1.2 standard deviations below the average. Similarly for Ricardo, Z = (11.8 - 12.4) / 0.9 = -0.67 (two decimal places). Ricardo's score is 0.67 standard deviations below the mean.

In statistical terms, a lower Z-score is better, which means Saul's time is better than Ricardo's because his Z-score is lower.

Learn more about Z-scores here:

https://brainly.com/question/33620239

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