14. At a BIG TEN College, two outstanding athletes, a 400-meter sprinter and a High Jumper, break their college's record in their respective events. Matthew, the college sports statistician, decides to determine which record-breaking result was more outstanding relative to the athlete's event. To determine who performed the more outstanding record breaking feat relative to their respective event, Matthew collected the best performances for each respective event within the BIG TEN Colleges for the year. The following table contains the information. Record Mean Standard Deviation Athlete | 400-Meter Sprinter 43.61 seconds 44.35 seconds 0.41 seconds High Jumper 2.44 meters 2.39 meters 0.04 meters a) Based on the table information, which athlete had the more outstanding record relative to their respective event? b) State the statistical result(s) you computed to support your answer!

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### Determining Outstanding Athletic Performance Relative to Events

At a BIG TEN College, two outstanding athletes, a 400-meter sprinter and a high jumper, broke their college records in their respective events. Matthew, the college sports statistician, aims to determine which record-breaking result was more outstanding relative to the athlete’s event. To ascertain this, Matthew analyzes the top performances recorded for each event within the BIG TEN College for the year. 

#### Collected Data:
Matthew compiled the following data for each athlete:

| Athlete               | Record          | Mean              | Standard Deviation      |
|-----------------------|-----------------|-------------------|-------------------------|
| 400-Meter Sprinter    | 43.61 seconds   | 44.35 seconds     | 0.41 seconds            |
| High Jumper           | 2.44 meters     | 2.39 meters       | 0.04 meters             |

#### Questions:
a) Based on the table information, which athlete had the more outstanding record relative to their respective event?  
b) State the statistical result(s) you computed to support your answer!

#### Analysis:
To determine which record is more outstanding, we compare the athletes’ performances using the z-score formula, which measures how many standard deviations an element is from the mean.

\[ \text{Z-score} = \frac{\text{Record} - \text{Mean}}{\text{Standard Deviation}} \]

- **400-Meter Sprinter:**

\[ \text{Z-score}_{\text{Sprinter}} = \frac{43.61 - 44.35}{0.41} = \frac{-0.74}{0.41} \approx -1.80 \]

- **High Jumper:**

\[ \text{Z-score}_{\text{Jumper}} = \frac{2.44 - 2.39}{0.04} = \frac{0.05}{0.04} = 1.25 \]

#### Conclusion:
For the 400-Meter Sprinter, a z-score of approximately -1.80 indicates that the record-breaking time is 1.80 standard deviations below the mean time, which is significantly faster. For the High Jumper, a z-score of 1.25 indicates that the record-breaking height is 1.25 standard deviations above the mean height.

Thus, **based on the z-scores**, the 400-meter sprinter had
Transcribed Image Text:### Determining Outstanding Athletic Performance Relative to Events At a BIG TEN College, two outstanding athletes, a 400-meter sprinter and a high jumper, broke their college records in their respective events. Matthew, the college sports statistician, aims to determine which record-breaking result was more outstanding relative to the athlete’s event. To ascertain this, Matthew analyzes the top performances recorded for each event within the BIG TEN College for the year. #### Collected Data: Matthew compiled the following data for each athlete: | Athlete | Record | Mean | Standard Deviation | |-----------------------|-----------------|-------------------|-------------------------| | 400-Meter Sprinter | 43.61 seconds | 44.35 seconds | 0.41 seconds | | High Jumper | 2.44 meters | 2.39 meters | 0.04 meters | #### Questions: a) Based on the table information, which athlete had the more outstanding record relative to their respective event? b) State the statistical result(s) you computed to support your answer! #### Analysis: To determine which record is more outstanding, we compare the athletes’ performances using the z-score formula, which measures how many standard deviations an element is from the mean. \[ \text{Z-score} = \frac{\text{Record} - \text{Mean}}{\text{Standard Deviation}} \] - **400-Meter Sprinter:** \[ \text{Z-score}_{\text{Sprinter}} = \frac{43.61 - 44.35}{0.41} = \frac{-0.74}{0.41} \approx -1.80 \] - **High Jumper:** \[ \text{Z-score}_{\text{Jumper}} = \frac{2.44 - 2.39}{0.04} = \frac{0.05}{0.04} = 1.25 \] #### Conclusion: For the 400-Meter Sprinter, a z-score of approximately -1.80 indicates that the record-breaking time is 1.80 standard deviations below the mean time, which is significantly faster. For the High Jumper, a z-score of 1.25 indicates that the record-breaking height is 1.25 standard deviations above the mean height. Thus, **based on the z-scores**, the 400-meter sprinter had
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