Using Excel 2010 to Find Probabilities for the Normal and ...
Using Excel 2010 to Find
Probabilities for the Normal and t
Distributions
A TUTORIAL
Using Excel with the Standard Normal, Normal,
and t distributions
? Standard Normal (¡°Z¡±)
?
?
Mean 0
Standard deviation 1
? ¡°Generic¡± Normal with
Normal
t(5)
mean and standard
deviation known
?
In ¡°olden days¡± we converted
these questions to ones about Z
? t (with specified degrees of
freedom)
?
Kim I. Melton, Ph.D.
Looks like ¡°normal¡± that is
slightly ¡°flatter¡±
University of North Georgia, Dahlonega, GA 30597
1
General Information
Applies to Normal and t Distributions
? Probability corresponds to area under a ¡°curve¡±
? Total area under a curve is 1
? Probability is found in one
of two ways:
?
?
Integration
Using tables (paper or electronic)
? We will focus on using tables
(actually electronic tables in Excel)!
Area under the curve corresponds to probability (and
all probabilities must be between 0 and 1)
-3
-2
-1
0
1
2
3
Z
Numbers along the base correspond to values of the variable (Z, X, or t) that can be thought
about as numbers on a number line. These numbers can range from -? to ?. The value of the
mean will appear under the peak of the distribution for these three distributions.
Kim I. Melton, Ph.D.
University of North Georgia, Dahlonega, GA 30597
2
Two types of questions
? If I have (name that) distribution, what proportion of
the observations will fall between ___ and ___. (or
what is the likelihood that a randomly selected value
will be between the same values)
?
This question asks you to find a probability from a distribution
with specific parameters
? If I have (name that) distribution, find the point that
will have ___% of the values above/below that point.
?
This question gives you a probability and asks you to find a
value for the variable.
Situation 2: Given ?, find b
Excel functions
end in ¡°inv¡±
?
b
?
Kim I. Melton, Ph.D.
University of North Georgia, Dahlonega, GA 30597
3
Situation 1: Given a and b, find P(a ................
................
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