Download Normal Distribution

T06-02 Normal & Standard Normal Templates
Purpose
T06-02 is an all in one template combining the features of the
two templates T06-02.N and T06-02.S allowing the analyst to
analyze the Normal and Standard 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/Z value depending upon a "Cumulative Probability". A
graphical representation of the Probability Scenario is also
shown.
Inputs
Mean & Standard Deviation
Normal or Standard Normal Distribution
Probability Scenario
Outputs
Probability Scenario Solution
Graph of Probability Scenario
T06-02 - 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 - 2
Standard Normal Distribution
A normal probability distribution describes many random processes
or continuous phenomena. It is the basis for classical statistical
inference.
f(X) =
f(X)


x

=
=
=
=
=
1
e
2
 X 2
 
 2
Frequency of random variable x
Population standard deviation
=
3.14159; e = 2.71828
Value of random variable (- < x < )
Population mean
=
1
0
T06-02 - 3
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 - 4
The Normal Distribution
mean and standard deviation
are entered here.
Probability scenarios
are automatically
calculated after X
values are entered.
Normal Distribution worksheet tab
T06-02 - 5
Normal & Standard Normal Distribution
This template allows you to calculate both Normal & Standard Normal
Distribution scenarios.
The previous slide shows the worksheet tab that for the template which
calculates the Normal Probability Distribution scenarios.
However, sometimes you may wish to calculate Standard Normal
Probability Distribution scenarios. In this case there are two options:
One:
You can use 0 and 1 as the mean and standard
deviation in the Normal Probability Distribution
Two:
You can use the second worksheet tab Standard
Normal shown on the next slide
The example demonstrates the Normal situation; however, the Standard
Normal situation works the same way.
T06-02 - 6
Probability scenarios
are automatically
calculated after Z
values are entered.
Standard Normal Distribution worksheet tab
T06-02 - 7
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 - 8
T06-02 - 9
The EXCEL Template also provides a
Normal Distribution Graph showing
the Probability Scenario.
T06-02 - 10
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 - 11
The EXCEL Template calculates
these answers much quicker than
looking them up in a table.
T06-02 - 12
The EXCEL Template also provides a
Normal Distribution Graph showing
the Probability Scenario.
T06-02 - 13
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 - 14
The EXCEL Template calculates
these answers much quicker than
looking them up in a table.
T06-02 - 15
The EXCEL Template also provides a
Normal Distribution Graph showing
the Probability Scenario.
T06-02 - 16
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 - 17
The EXCEL Template calculates
these answers much quicker than
looking them up in a table.
Caution: In using this portion of
the template, you must enter the
problem such that the input is the
Cumulative Probability.
T06-02 - 18
The EXCEL Template also provides a
Normal Distribution Graph showing
the Probability Scenario.
T06-02 - 19