The Normal Random Variable's Density Function Is (1) Single-Peaked Above

The normal random variable's density function is (1) single-peaked above the variable's mean, median, and mode, all of which are equal to one another, (2) perfectly symmetric about this peaked central value and, thus, bell-shaped, and (3) characterized by tails extending indefinitely in both directions from the center, approaching (but never touching) the horizontal axis, which implies a positive probability for finding values of the random variable anywhere between minus infinity and plus infinity.