A successful basketball player has a height of 6 feet 11 inches, or 211 cm. Based on statistics from a data set, his height converts to the z score of 5.17. How many standard deviations is his height above the mean? The player’s height is standard deviation(s) above the mean. (Round to two decimal places as needed.) Conter sible Reso Incor If your score on your next statistics test is converted to a z score, which of these z scores would you prefer – 2.00, -1.00,0,1.00, 2.00? Why? O A. The z score of -1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score. OB. The z score of -2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores O C. The z score of 200 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores OD. The z score of O is most preferable because it corresponds to a test score equal to the mean. O E. The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score.
The Correct Answer and Explanation is :
To address your query in two parts:
Part 1: Understanding the Basketball Player’s Z Score
Given that the basketball player’s height of 211 cm corresponds to a z-score of 5.17, this directly tells us how many standard deviations his height is above the mean. A z-score of 5.17 means that the player’s height is 5.17 standard deviations above the average height in the dataset used. There’s no need for additional calculations; the z-score itself explicitly indicates this.
Part 2: Choosing the Preferable Z Score for a Statistics Test
When evaluating z-scores for a statistics test, it’s important to understand that:
- A z-score of 0 represents a score exactly at the mean.
- Positive z-scores indicate performance above the mean.
- Negative z-scores represent scores below the mean.
Therefore, among the options provided:
- Option A (-1.00): Incorrect because a score below the mean is not above average.
- Option B (-2.00): Incorrect as it is even further below the mean, indicating a poorer performance.
- Option C (2.00): Correct. A z-score of 2.00 signifies a score that is two standard deviations above the mean, placing it higher than a large percentage of the other scores.
- Option D (0): This indicates an average score, which is not preferable if the aim is to achieve a high score.
- Option E (1.00): Also a good option, indicating a score above the mean, but not as high as a z-score of 2.00.
Correct Answer: C. The z-score of 2.00 is most preferable because it is 2.00 standard deviations above the mean, which would correspond to one of the highest test scores among the options.
Explanation:
Choosing a higher z-score in the context of test scores translates to better performance relative to the peer group. A z-score of 2.00 not only demonstrates an above-average ability but also places the test taker in a high percentile rank among peers. This could be crucial for competitive exams where ranking relative to peers can determine qualification or selection. In summary, a z-score of 2.00 in this context means achieving a score significantly better than the majority, thus maximizing one’s chances for favorable outcomes like scholarships, admissions, or other accolades dependent on test performance.
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