Characteristics of Normal Distribution Curve

A normal distribution curve is a bell-shaped, symmetrical curve that is uni-modal, where the mean, median, and mode are all equal and located at the center. The curve’s tails approach but never touch the horizontal axis (asymptotic), and its spread is determined by the standard deviation.

A normal distribution curve with mean μ and standard deviation has the following characteristics:

1. The mean, median, and mode are equal. 50% of all values are below the mean and 50% are above it.
2. The normal curve is bell-shaped and symmetric about its mean μ.
3. The total area under the normal curve is 1.
4. Normal curves extend endlessly in both directions, but the curve becomes so close to zero for values of the random variable that are more than 4 standard deviations above or below the mean that the area is negligible.

5. The normal curve changes its curvature from a “cup” shape to a “cap” shape or vice-versa at one standard deviation below and above the mean. These points are called inflection points.