Normal Distribution

Normal Distribution is a quantitative phenomena. Many measurements can be approximated by the normal distribution. Normal distribution is also known as Gaussian distribution. The standard normal distribution is normal distribution with a mean of zero and variance of one. Normal distribution is the most commonly observed probability distribution. Many measurements conform to the normal distribution. The shape of the normal distribution resembles that of a bell so it is known as bell curve. The normal distribution is defined by two parameters: the mean and the standard deviation. The normal distribution is frequently used to describe random variables.

The shape of the normal probability distribution is symmetric and the tails of the curve extend to infinity in both directions and theoretically never touch the horizontal axis.

The mean of the distribution can be any numerical value - negative, zero, or positive value. The highest point of the curve is at the mean. The standard deviation determines the width of the curve so larger values result in wider and flatter curves. The total area under the curve for the normal probability distribution is one.

Commonly used intervals:

68.28% of the time a normal random variable assumes a value within plus or minus one standard deviation of its mean

95.44% of the time a normal random variable assumes a value within plus or minus two standard deviations of its mean

99.72% of the time a normal random variable assumes a value within plus or minus three standard deviations of its mean