Final answer:
Without specific values for the mean and standard deviation of American men's heights, we cannot determine the exact percentage of men between 68.7 and 69.3 inches tall.
Step-by-step explanation:
The question focuses on finding what percentage of American men are between 68.7 and 69.3 inches tall. This problem involves understanding the properties of a normal distribution, as human heights typically follow this pattern. The given statistics suggest a normal distribution with a mean (μ) and a standard deviation (σ). However, specific values for these parameters are not provided in the information given. The percentages of heights in certain ranges, especially around a mean, would usually be derived using a normal distribution curve and Z-scores which are not provided. Therefore, without further information regarding the mean and standard deviation of the heights for American men, we cannot accurately answer this question.