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Section 5.1 ~
What is Normal?
Introduction to Probability and Statistics
Ms. Young ~ room 113
Sec. 5.1
Objective

In this section you will understand what is meant by a
normal distribution and be able to identify situations
in which a normal distribution is likely to arise.
Sec. 5.1
Normal Distribution

A normal distribution has the following characteristics:
Single-peaked
 Symmetric (mean and median are the same as the mode)
 The curve is spread out in the shape of a bell (“bell-shaped”
distribution)

Sec. 5.1
Normal Distribution Cont’d…



All normal distributions have the same characteristic bell shape, but
can differ in their mean and variation
Knowing the mean and the standard deviation of a normal distribution
tells you everything you need to know about its variation
The following distributions have the same mean, but different standard
deviations
Sec. 5.1
The Normal Distribution and Relative Frequencies


The area that lies under the curve corresponding to a range of
values on the x-axis is the relative frequency of those values
The total area under the curve is 1, or 100% because the total
relative frequency for the histogram is 1 or 100%
Sec. 5.1
When Can We Expect a Normal Distribution?

Here are some common circumstances in which you can expect a
normal distribution to occur:

Physical characteristics such as:


Standardized test scores such as:


Height, weight, blood pressure, & reflex times
SAT’s, IQ tests, PSSA’s, etc.
Sports statistics such as:

Batting averages, times in swimming, results in a track meet, etc.
Sec. 5.1
Summary

A distribution is likely to be normal if it satisfies the following
criteria:
Most data values are clustered near the mean, giving the
distribution a well defined single peak
 Data values are spread evenly around the mean, making the
distribution symmetric
 Larger deviations from the mean become increasingly rare,
producing tapering tails of the distribution (therefore creating the
bell shape)
 Individual data values result from a combination of many different
factors, such as genetic and environmental factors
