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QM 2113 -- Fall 2003
Statistics for Decision Making
Probability Applications: The Normal
Distribution
Instructor: John Seydel, Ph.D.
Student Objectives
Discuss the characteristics of normally
distributed random variables
Calculate probabilities for normal
random variables
Apply normal distribution concepts to
practical problems
Administrative Items
Exam1 rework: haven’t completed the grading
Grading scheme (clarification/correction)


300 points: Exercises & quizzes
100 points: Midterm exam
 Actually 3 midterm exams
 Grade will be the best of the three
 Next one: October 20 (bivariate analysis, probability
distributions, sampling concepts, intro to inference)

200 points: Final exam (comprehensive)
Collect homework: exercises from text
Now, a Review
What is probability?
What’s a probability distribution?
What are some basic rules for working with
probability?




Basic notation
Range of possible values
Complement rule
Additive rules
 All possible events
 More than one event
What do we mean by a “normal distribution”?
Questions About the Homework?
Data analysis (Web Analytics case)


Univariate
Bivariate
 Quantitative variables
 Qualitative variables
Normal distribution problems



Basic calculations (1, 2)
Applications (4, 5)
Understanding the concepts (35, 36)
If Something’s Normally Distributed
It’s described by


m (the population/process average)
s (the population/process standard deviation)
Histogram is symmetric


Thus no skew (average = median)
So P(x < m) = P(x > m) = . . . ?
Shape of histogram can be described by
f(x) = (1/s√2p)e-[(x-m)2/2s 2]
We determine probabilities based upon
distance from the mean (i.e., the number of
standard deviations)
A Sketch is Essential!
Use to identify regions of concern
Enables putting together results of
calculations, lookups, etc.
Doesn’t need to be perfect; just needs
to indicate relative positioning
Make it large enough to work with;
needs annotation (probabilities,
comments, etc.)
Keep In Mind
Probability = proportion of area under the
normal curve
What we get when we use tables is always the
area between the mean and z standard
deviations from the mean
Because of symmetry
P(x > m) = P(x < m) = 0.5000
Tables show probabilities rounded to 4 decimal
places


If z < -3.89 then probability ≈ 0.5000
If z > 3.89 then probability ≈ 0.5000
Theoretically, P(x = a) = 0
P(30 ≤ x ≤ 35) = P(30 < x < 35)
Additional Exercises
Refer to review handout for OM class



Project planning
Process capability analysis
Inventory planning
From text


Airline flight management (#7)
Theatre concessions planning (#13-15)
Summary of Objectives
Discuss the characteristics of normally
distributed random variables
Calculate probabilities for normal
random variables
Apply normal distribution concepts to
practical problems