Final answer:
The line that goes through the mean on a normal distribution curve is called the line of symmetry or the mean line, and it is central to the distribution's properties.
Step-by-step explanation:
The line that goes through the mean of a normal distribution curve is known as the line of symmetry or the mean line. It is a vertical line that intersects the x-axis at the mean value (μ). Since the normal distribution is symmetrical, the mean, median, and mode all coincide at the same point on the curve, which lies at the center of the distribution. In a normal distribution, any change in the mean (μ) shifts the entire graph left or right, while changes in the standard deviation (σ) affect the spread or width of the curve. The total area under the curve is always equal to one, which confirms that the distribution represents a probability distribution. The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1.