Step 1 :Given that the mean height for men is 69.5 inches and the standard deviation is 3.6 inches, we need to find the percentage of men whose height falls within the range of 57 to 64 inches.
Step 2 :To do this, we calculate the z-scores for these heights. The z-score is calculated as \((X - \mu) / \sigma\), where X is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
Step 3 :Calculating the z-scores for the minimum and maximum heights gives us -3.4722222222222223 and -1.5277777777777777 respectively.
Step 4 :We then find the area under the normal distribution curve between these z-scores, which gives us the percentage of men who meet the height requirement.
Step 5 :The percentage of men who meet the height requirement is found to be 6.302577629916504.
Step 6 :Rounding this to two decimal places, we get \(\boxed{6.30\%}\).
Step 7 :This suggests that most of the characters at the amusement park are likely not men, as only a small percentage of men meet the height requirement.