Bernard Szlachta: /* Example */

2014-06-03T10:49:55Z

Example

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{{Cat|Normal Distribution| 01}}
*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==
:[[File:ClipCapIt-140602-143925.PNG]]
=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=
:[[File:ClipCapIt-140602-141815.PNG]]
* 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==
:[[File:ClipCapIt-140602-143745.PNG]]

=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 display=simple >
{ Which are other names for the normal distribution? Select all that apply.

|type="[]"}
-Typical curve
+Gaussian curve
-Regular distribution
-Galileo curve
+Bell-shaped curve
-Laplace's distribution

{
{{Show Answer|
Gaussian curve, Bell-shaped curve
}}
}

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

|type="[]"}
+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.

{
{{Show Answer|
A,B,D
}}
}

</quiz>

Introduction to Normal Distributions - Revision history

Bernard Szlachta: /* Example */