The smallest EGC permitted to be installed in the conduit between the panel and the pull box for a 250-amp breaker is ___ AWG.

The correct choice specifies that the smallest equipment grounding conductor (EGC) permitted to be installed in the conduit between a panel and a pull box for a 250-amp breaker is 3 AWG. This is determined based on the National Electrical Code (NEC) requirements, which establish conductor sizing for equipment grounding to ensure safety in electrical installations.

According to NEC Table 250.122, the minimum size of the EGC is based on the rating of the overcurrent protection device, in this case, the 250-amp breaker. For a circuit breaker rated at 250 amps, the NEC dictates that a 3 AWG copper conductor or a larger size must be used for the EGC. This ensures adequate grounding to prevent electrical shock hazards and facilitate the safe operation of circuit protection devices.

In the context of the other wire sizes, options such as 6 AWG, 8 AWG, and 4 AWG do not meet the NEC requirements for a 250-amp breaker, as they are under the minimum designated size. Using an appropriately sized EGC is critical for effective fault current path and grounding, highlighting the importance of adherence to these safety standards in electrical installations.