Final answer:
The correct explanation is that the Appalachian Mountains are older than the Rocky Mountains and have been subjected to greater weathering and erosion, reducing their peak heights.
Step-by-step explanation:
The Appalachian Mountains are older than the Rocky Mountains and have been exposed to weathering and erosion for a much longer period of time. The formation of the Appalachians involved multiple tectonic events such as the Taconic, Acadian, and Alleghenian orogenies and subsequent erosion that reduced their height over the millions of years. On contrast, the main growth of the Rockies happened later during the Laramide Orogeny and while also subjected to erosion, they have not been worn down as extensively as the Appalachians. Therefore, the best explanation for the difference in average peak height between the two mountain ranges is that the Appalachian Mountains are older and have been subjected to greater weathering and erosion, decreasing their height.