Final answer:
To compare the height of a boy at the 10th percentile with the mean height of 17-year-old boys, we need to find the z-score corresponding to the 10th percentile and use it to calculate the height.
Step-by-step explanation:
To compare the height of a boy at the 10th percentile with the mean height of 17-year-old boys, we need to find the z-score corresponding to the 10th percentile. From the given information, we know that the heights of 17-year-old boys are normally distributed with a standard deviation of 2.25 inches.
Using the standard normal distribution table, a z-score of -1.28 corresponds to the 10th percentile. To find the height, we can use the formula:
Height = Mean + (z-score * Standard Deviation) = Mean + (-1.28 * 2.25)