Final answer:
When multiple EPSPs arrive at a neuron at the same time, they can summate to sufficiently depolarize the neuron to reach the threshold of excitation and trigger an action potential, provided they outweigh any IPSPs.
Step-by-step explanation:
When many excitatory postsynaptic potentials (EPSPs) arrive at the same neuron simultaneously, the process known as summation occurs. This leads to the depolarization of the postsynaptic neuron's membrane. If the summation of EPSPs is significant enough to overcome any concurrent inhibitory postsynaptic potentials (IPSPs) and reach the threshold of excitation, the neuron will fire an action potential. This integration of signals happens at the axon hillock, where the neuron assesses the net effect of all excitatory and inhibitory inputs.
An example of this would be if a postsynaptic neuron receives five synapses that cause different graded potentials: three synapses induce EPSPs, and two cause IPSPs. If the combined EPSPs produce a sufficiently large net depolarization to shift the postsynaptic membrane voltage from the resting potential (typically around -70 mV) to the threshold level (usually around -55 mV), the neuron will fire. This combined effect acts as a filter to ensure only significant and important information is transmitted through the nervous system, avoiding transmission of random "noise."