# Statistics for Decision Makers - 07.01 - Normal Distributions

From Training Material

- Title
- 07.01 - Normal Distributions
- Author
- Bernard Szlachta (NobleProg Ltd) bs@nobleprog.co.uk
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- www.NobleProg.co.uk
- Subfooter
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## Contents

## Normal Distributions。

- Most of the statistical analyses presented are based on the bell-shaped or normal distribution
- We learn how to calculate 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 - A
**binomial distribution**is used for**discrete**variables - A
**normal distribution**is for**continuous**variables

# Bell Curve。

- "Gaussian curve" (μ = 0, σ = 1)
- Although Gauss played an important role in its history, de Movire first discovered the normal distribution
- There is no single "the normal distribution" since there are many normal distributions which differ in their means and standard deviations
- Normal distributions can differ in their means and in their standard deviations
- The distributions below, as well as all other normal distributions, are symmetric with relatively more values at the centre of the distribution and relatively few in the tails

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

# The density of the normal distribution。

- The density of the normal distribution (the height for a given value on the x axis) is shown above
- 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
- Since this is a non-mathematical treatment of statistics, do not worry if this expression confuses you

## Normal Cumulative Distribution。

=NORMDIST(1,0,1,true) = 0.8413447461

# Features of Normal Distributions。

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

# Quiz。

# Quiz