Final answer:
To determine the height based on a z-score, the mean and standard deviation of the reference group's heights are required. The z-score indicates how many standard deviations above or below the mean the individual's height is. For instance, a z-score of 1.27 would mean the height is 1.27 standard deviations above the mean of the group.
Step-by-step explanation:
Calculating a person's height based on their z-score requires having the mean and standard deviation of the heights for that specific age group. The z-score formula, which is z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation, helps to identify how many standard deviations an individual's height is from the mean height.
For example, suppose a 15-to 18-year-old male from Chile had a height with a z-score of 1.27. If the mean height for this age group is known, as well as the standard deviation, we could calculate the exact height by rearranging the formula to X = zσ + μ. This calculation would show that the individual's height is 1.27 standard deviations above the mean. Similarly, if the NBA player's height is 77 inches with a z-score of -0.5141, this height is 0.5141 standard deviations below the mean NBA player height.