Final answer:
The component that does NOT influence the likelihood of an action potential at the axon hillock is the strength of the incoming action potential since action potentials are 'all or none' events and do not vary in strength.
Step-by-step explanation:
The question pertains to the factors influencing the likelihood of stimulating an action potential at the axon hillock in a neuron. The correct answer that does NOT influence this process is d. The strength of the incoming action potential. Action potentials are 'all or none' events that either occur fully once they reach the threshold potential at the axon hillock, or they do not occur at all if the threshold isn't reached. The strength of an individual action potential does not vary; rather, stronger stimuli might cause action potentials to occur more frequently. Factors such as the type of stimulus (excitatory or inhibitory), location relative to the axon hillock, relative timing of stimuli, and the number of stimuli can influence the membrane potential and whether it reaches the threshold needed to generate an action potential.
Graded potentials, including EPSPs and IPSPs, can summate temporally or spatially at the axon hillock to reach the threshold. EPSPs can depolarize the membrane, while IPSPs hyperpolarize the membrane; it's the net effect that determines if the threshold is reached. Voltage-gated Na+ channels play a key role in initiating the depolarizing phase of the action potential within these regions.