Given a set of measurements with finite variance, the Gaussian (normal) distribution is the maximum-entropy distribution consistent with that variance — the most conservative assignment of probabilities when only the variance is known. By the law of large numbers, repeated draws from such a system tend to converge toward this maximum-entropy shape. As a rule of thumb, a flatter, lower-peaked Gaussian curve corresponds to higher entropy, since probability mass is spread more evenly across outcomes; a taller, narrower peak corresponds to lower entropy, since outcomes cluster more tightly around a few values.