Final answer:
Grant Hill has the highest score with 25.8 points. Z-scores for heights of 77 inches and 85 inches are calculated as -0.51 and 1.54 respectively. Extreme z-scores, like 3.5, for a player's height are unlikely and would be met with skepticism.
Step-by-step explanation:
The student is asking which basketball player has the highest score based on the given data:
- Scottie Pippen: 12.5
- Grant Hill: 25.8
- Robert Horry: 5.7
- Juwan Howard: 14.9
- Jalen Rose: 18.2
By simply comparing the scores, it is clear that Grant Hill has the highest score with 25.8. Therefore, the correct answer is a) Grant Hill.
Z-Scores Calculation
To calculate the z-scores for the heights given, you use the formula:
Z = (X - μ) / σ
Where X is the value from the data, μ is the mean, and σ is the standard deviation.
- For 77 inches:
Z = (77 - 79) / 3.89 = -0.51 - For 85 inches:
Z = (85 - 79) / 3.89 = 1.54
A z-score of -0.51 means 77 inches is 0.51 standard deviations below the mean height, while a z-score of 1.54 means 85 inches is 1.54 standard deviations above the mean height.
If a player claims a z-score of 3.5 for his height, we would be skeptical. A z-score of 3.5 is extremely high and corresponds to a value that is 3.5 standard deviations above the mean. Given that heights have a normal distribution, this would place him in a very small percentage of players, making it questionable.