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```T06-02.N Normal Distribution Graphical
Purpose
Allows the analyst to analyze the Normal Probability
Distribution. Probability Scenario's are calculated for
"between", "greater than", and "less than" eliminating
the need to perform calculations to use Standard
Normal Distribution Tables. The template also allows
the analyst to determine an X value depending upon a
"Cumulative Probability". A graphical representation of
the Probability Scenario is also shown.
Inputs
Mean & Standard Deviation of Normal Distribution
Probability Scenario
Outputs
Probability Scenario Solution
Graph of Probability Scenario
T06-02.N - 1
Normal Distribution
A normal probability distribution describes many random processes
or continuous phenomena. It is the basis for classical statistical
inference.
1
f(X) =
e
 2
f(X)


x

=
=
=
=
=
 X-   2


 2 
Frequency of random variable x
Population standard deviation
3.14159; e = 2.71828
Value of random variable (- < x < )
Population mean
T06-02.N - 2
Battery Example
A manufacturer of batteries claims that the average length
of life for its grade A batteries is 60 months. Suppose the
standard deviation of the life-length is 10 months and the
frequency distribution of the life-length data is normally
distributed. What is the probability that the batteries last
a.
b.
c.
d.
Less than 52 months
More than 82 months
Between 42 and 77 months
Determine the battery life such that the probability less
than the battery life is equal to .8400?
T06-02.N - 3
Normal Distribution - Battery Example
.2119
0
20
40
60
80
100
120
52
What is the probability that the batteries last
a. Less than 52 months .2119
T06-02.N - 4
Input the mean, standard deviation, & probability scenario, and the
answer and graph for the Normal Distribution probability scenario
are automatically calculated
T06-02.N - 5
Normal Distribution - Battery Example
.0139
0
20
40
60
80
82
100
120
What is the probability that the batteries last
b. More than 82 months
.0139
T06-02.N - 6
Input the mean, standard deviation, & probability scenario, and the
answer and graph for the Normal Distribution probability scenario
are automatically calculated
T06-02.N - 7
Normal Distribution - Battery Example
.9195
0
20
40
60
80
100
120
42
77
What is the probability that the batteries last
c. Between 42 and 77 months
.9195
T06-02.N - 8
Input the mean, standard deviation, & probability scenario, and the
answer and graph for the Normal Distribution probability scenario
are automatically calculated
T06-02.N - 9
Normal Distribution - Battery Example
0
20
40
60
69.945
80
100
120
Determine the battery life such that the
probability less than the battery life is equal to
.8400? In other words,
What is the value of X such that CP(X) <= .8400? 69.945
T06-02.N - 10
Input the mean, standard deviation, & probability scenario, and the
answer and graph for the Normal Distribution probability scenario
are automatically calculated
Caution: In using
this portion of the
template, you must
enter the problem
such that the input is
the Cumulative
Probability.
T06-02.N - 11
```
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