Which of the following limitations applies to a private pilot?

A private pilot is prohibited from acting as pilot in command of an aircraft carrying passengers or property for compensation or hire. This limitation is central to the definition of a private pilot certificate; it is designed for individuals who fly for personal or recreational purposes, rather than for commercial gain. Therefore, the correct choice reflects this fundamental restriction, which emphasizes that private pilots may not receive payment for flying activities involving passengers.

Other options that suggest private pilots can operate for hire or carry passengers for a fee contradict the regulatory framework established by the FAA for private pilot conduct. Additionally, private pilots are not authorized to operate high altitude airplanes without obtaining the necessary endorsements or certificates, which means that claim does not align with established flight operation standards.