Final answer:
The basketball player's height of 6 feet 4 inches with a z-score of 2.66 means his height is 2.66 standard deviations above the mean height. The correct answer is a. 2.66 standard deviations.
Step-by-step explanation:
The student's question involves the concept of a z-score, which is a statistical measurement that describes a value's relationship to the mean of a group of values. In this case, a basketball player's height of 6 feet 4 inches, which converts to 193 cm, has been given a z-score of 2.66. This means that the player's height is 2.66 standard deviations above the mean height. Given this information, the correct answer to the question is a. 2.66 standard deviations.
As an example, to calculate the z-score for a height of 77 inches, you would use the z-score formula: z = (X - μ) / σ, where X is the value (height), μ (mu) is the mean, and σ (sigma) is the standard deviation. If the mean (μ) is 79 inches and the standard deviation (σ) is 3.89 inches, the z-score would be z = (77 - 79) / 3.89 = -0.5141, indicating that a height of 77 inches is 0.5141 standard deviations below the mean.