To be eligible to operate in either the normal or utility category, Piper model PA22-150, serial number 22-4450, must have which of the following installed?

To operate a Piper model PA22-150 in either the normal or utility category, having the appropriate control modification kit installed is essential. This kit is designed to enhance the aircraft's performance and compliance with regulatory requirements specific to its operational category. The control modifications ensure that the aircraft meets safety and operational standards necessary for the designated category of use.

The other options may pertain to various operational considerations or equipment for the aircraft, but they do not serve the primary function of categorizing the aircraft as either normal or utility. For instance, the specifications for the propeller or the placard regarding seat capacity address performance aspects or safety labels but do not change the airworthiness categorization itself. Similarly, while a weight and balance report is critical for flight planning and ensuring safe operation, it does not directly relate to the aircraft's eligibility for a specific operational category. Therefore, having the control modification kit is the accurately vital requirement for determining the aircraft's eligibility to operate in the specified categories.