Introduction to Normal Distributions

• Most of the statistical analyses presented are based on the bell-shaped or normal distribution
• Methods for calculating probabilities based on the normal distribution
• A frequently used normal distribution is called the Standard Normal distribution (AKA Gauss Distribution)
• The binomial distribution can be approximated by a normal distribution

Bell Curve

• Gaussian curve is a special case of a Normal Distribution (μ = 0, σ = 1)
• Although Gauss played an important role in its history, de Moivre first discovered the normal distribution
• There is no "the normal distribution" since there are many normal distributions which differ in their means and standard deviations

Probability Density Function

=NORMDIST(1,0,1,FALSE) = 0.2419707245

• All normal distributions are symmetric with relatively more values at the centre of the distribution and relatively few in the tails

The density of the normal distribution

• The density of the normal distribution is the height for a given value on the x axis
• The parameters μ and σ are the mean and standard deviation, respectively, and define the normal distribution
• The symbol e is the base of the natural logarithm and π is the constant pi.

Normal Cumulative Distribution

Features of Normal Distributions

1. Normal distributions are symmetric around their mean.
2. The mean, median, and mode of a normal distribution are equal.
3. The area under the normal curve is equal to 1.0.
4. Normal distributions are denser in the center and less dense in the tails.
5. Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).
6. 68% of the area of a normal distribution is within one standard deviation of the mean.
7. Approximately 95% of the area of a normal distribution is within two standard deviations of the mean.

Quiz

1 Which are other names for the normal distribution? Select all that apply.

	Typical curve
	Gaussian curve
	Regular distribution
	Galileo curve
	Bell-shaped curve
	Laplace's distribution

Answer >>

Gaussian curve, Bell-shaped curve

2 Select all of the statements that are true about normal distributions.

	A:They are symmetric around their mean.
	B:The mean, median, and mode are equal.
	C:They are defined by their mean and skew.
	D:The area under the normal curve is equal to 1.0.
	E:They have high density in their tails.
	F:They are discrete distributions.

Answer >>

A,B,D