The hot wire in a standard three-wire electrical system is typically yellow. This is because the National Electrical Code (NEC) in the United States designates yellow as the color for the hot wire in residential and commercial installations. Blue and gray are not designated as standard colors for hot wires in the NEC.

The NEC is a set of guidelines and standards for electrical installations in the United States, and it is widely followed by electricians and code inspectors. The use of specific colors for different types of wires helps to ensure safety and clarity during installation and maintenance. Yellow is chosen for the hot wire because it is easily distinguishable from the other two wires in the system: the neutral wire, which is typically white, and the ground wire, which is typically green or bare copper.

According to the NEC Article 200.6(A), "Wiring Methods," the colors of conductors shall be as follows: 'Conductors shall be identified by color as follows: (1) Hot conductors shall be identified by a continuous color band or by color coding.' This standard clearly indicates that the hot wire should be yellow.

In addition to the NEC, the American Wire Gauge (AWG) system also plays a role in wire identification. The AWG is a standardized wire size system used in the United States and Canada. While the AWG does not specify wire colors, it does provide a consistent way to identify wire sizes, which can be important for determining the appropriate wire for a given application.

In summary, the hot wire in a standard three-wire electrical system is yellow, as specified by the National Electrical Code. This color-coding system is in place to enhance safety and ease of installation and maintenance.