Transcript Week_2_-_MBA510_Mana..

MBA / 510
Managerial Decision Making
Facilitator: René Cintrón
Week 2 - Objectives
• Analyze data using descriptive statistics
• Apply basic probability concepts to
facilitate business decision making
• Distinguish between discrete and
continuous probability distributions
• Apply the normal distribution to
facilitate business decision making.
Analyze data using descriptive
statistics
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Population mean
Sample mean
Weighted mean
Median
Mode
Variance and standard deviation
Empirical rule
Mean, Median, Mode
• The mean is the usual average
• The median is the middle value
• The mode is the number that is
repeated more often than any other
Bell -Shaped Curve showing the relationship between  and .
68%
95%
99.7%
-3
-2 -1

+1 +2 + 3
3- 6
Empirical Rule: For any symmetrical, bellshaped distribution:
About
68% of the observations will lie within 1s
the mean
About
95% of the observations will lie within 2s of
the mean
Virtually
the mean
all the observations will be within 3s of
Basic Probability Concepts
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What is a probability?
Approaches to assigning probabilities
Rules for computing probabilities
Contingency tables
There are three definitions of probability: classical,
empirical, and subjective.
The
Classical
definition
applies when
there are n
equally likely
outcomes.
The Empirical
definition applies
when the number
of times the event
happens is
divided by the
number of
observations.
Subjective
probability is
based on
whatever
information is
available.
An Outcome is
the particular
result of an
experiment.
An Event is
the collection
of one or more
outcomes of an
experiment.
Experiment: A fair die is cast.
Possible outcomes: The
numbers 1, 2, 3, 4, 5, 6
One possible event: The
occurrence of an even
number. That is, we collect
the outcomes 2, 4, and 6.
Mutually Exclusive Events
Events are Mutually
Exclusive if the
occurrence of any one
event means that none
of the others can occur
at the same time.
Mutually exclusive:
Rolling a 2 precludes
rolling a 1, 3, 4, 5, 6
on the same roll.
Events are Independent
if the occurrence of one event
does not affect the occurrence
of another.
Independence: Rolling a 2
on the first throw does not
influence the probability of
a 3 on the next throw. It is
still a one in 6 chance.
Events are Collectively Exhaustive if at
least one of the events must occur when an
experiment is conducted.
Empirical Example
Throughout her
teaching career
Professor Jones has
awarded 186 A’s out
of 1,200 students.
What is the
probability that a
student in her
section this
semester will
receive an A?
This is an example of the
empirical definition of
probability.
To
find the probability a
selected student earned an A:
186
P( A) 
 0.155
1200
Examples of subjective probability are:
estimating the probability the
New Orleans Saints will win the
Super Bowl this year.
es t i m at i n g t h e p r o b a b i l i t y
mortgage rates for home loans
will top 8 percent.
If two events
A and B are mutually
exclusive, the
Special Rule of
Addition states that the
Probability of A or B
occurring equals the sum of
their respective
probabilities.
P(A or B) = P(A) + P(B)
The Complement Rule
The Complement Rule is used to determine the
probability of an event occurring by subtracting the
probability of the event not occurring from 1.
If P(A) is the probability of event A and P(~A) is
the complement of A,
P(A) + P(~A) = 1 or P(A) = 1 - P(~A).
The Special Rule of Multiplication
requires that two events A and B are independent.
Two
events A and B are independent if the
occurrence of one has no effect on the probability of
the occurrence of the other.
This
rule is written:
P(A and B) = P(A)P(B)
A Joint Probability measures the likelihood
that two or more events will happen concurrently.
An example would
be the event that a
student has both a
stereo and TV in his
or her dorm room.
A Conditional Probability is the
probability of a particular event occurring,
given that another event has occurred.
The probability of
event A occurring
given that the event
B has occurred is
written P(A|B).
The General
Rule of
Multiplication is
used to find the joint
probability that two
events will occur.
It states that for two
events A and B, the
joint probability that
both events will happen
is found by multiplying
the probability that
event A will happen by
the conditional
probability of B given
that A has occurred.
Discrete and Continuous
Probability Distributions
• What is a probability distribution?
• Discrete probability distributions
• Random variables
• Discrete random variable
• Mean, variance, and standard deviation of
a probability distribution
• Continuous probability distributions
• Continuous random variable
Probability Distributions
A listing of all
possible outcomes
of an experiment
a n d
t h e
corresponding
probability.
Types of Probability
Distributions
Discrete probability Distribution
Can assume only certain
outcomes
Random variable Continuous Probability Distribution
A numerical value Can assume an infinite number of
values within a given range
determined by the
outcome of an
experiment.
Continuous Probability Distribution
Discrete Probability Distribution
The sum of the
probabilities of
the various
outcomes is 1.00.
The outcomes
are mutually
exclusive.
The probability
of a particular
outcome is
between 0 and
1.00.
The number of
students in a class
The number of
cars entering a
carwash in a hour
The number of
children in a family
Normal Distribution
• Family of normal probability
distributions
• Standard normal distribution
• Empirical rule
• Finding areas under the normal curve
The Normal probability distribution
is bell-shaped and has a single peak at the
center of the distribution.
Is
symmetrical about the mean.
is
asymptotic.
That is the curve gets closer and
closer to the X-axis but never actually touches it.
, to determine its location and
its standard deviation, , to determine its
Has
its mean,
dispersion.
r
a
l
i
t r
b
u
i o
n
:

=
0
,
2
=
1
Characteristics of a Normal Distribution
0
. 4
Normal
curve is
symmetrical
. 3
0
. 2
0
. 1
f ( x
0
Theoretically,
curve extends to
infinity
. 0
- 5
a
Mean, median, and
mode are equal
x
Variance and Standard Deviation
2

s2
=
=

2
 (X - )2
N

(X - X)2
n-1
s s
2
The Standard Normal
Probability Distribution
The standard normal
distribution is a normal
distribution with a mean of 0
and a standard deviation of 1.
It is also called the
z distribution.
A z-value is the distance between a selected value,
designated X, and the population mean , divided by
the population standard deviation, . The formula is:
z
X -

3- 30
Empirical Rule: For any symmetrical, bellshaped distribution:
About
68% of the observations will lie within 1s
the mean
About
95% of the observations will lie within 2s of
the mean
Virtually
the mean
all the observations will be within 3s of
About 68 percent of
the area under the
normal curve is within
one standard deviation
About 95 percent is within two
of the mean.
standard deviations of the mean.
 + 1
 + 2
Practically all is within three standard
deviations of the mean.
 + 3
Areas Under the Normal
Curve
Bell -Shaped Curve showing the relationship between  and .
68%
95%
99.7%
-3
-2 -1

+1 +2 + 3
Next Week
• Apply inferential statistics in solving
business problems
• Determine an appropriate sample size
• Apply confidence intervals in solving
business problems.
• Problem Sets
• Team Business Problem Proposal