MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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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