Transcript BA 275, Fall 1998 Quantitative Business Methods

BA 275
Quantitative Business Methods
Agenda
 Experiencing Random Behavior
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Binomial Experiment
Binomial Probability Distribution
Normal Probability Distribution
 Quiz #3
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Midterm Exam #1
 Wednesday, 2/01/06 in class.
 Closed books/notes/packet/friends exam, but I will provide you
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The empirical rule
The binomial formula
The normal table
 Need a good night sleep and a calculator that WORKS!
 Topics:
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Describing Categorical/Numerical Data
The Empirical Rule and Box plot
Binomial Distribution
The Normal Distribution and the Central Limit Theorem
 CyberStats: A-1, A-4, A-5, A-6, A-9, B-7, B-9, B-11, B-12.
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Example
 Ialpha, a manufacturer of disk drives, buys power
switches from a vendor. Ialpha wishes to have fewer
than 5% defective switches. To determine whether to
accept or reject a shipment, the company decides to
inspect 20 power switches and reject the shipment if
more than one is defective.
 Suppose that, in fact, 11% of the switches are
defective. What is the chance that Ialpha will accept
the shipment?
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High Speed Internet Connection
 Claim 1:
% of college students who have high speed
internet connection is 75%
 Claim 2:
 % of college students who have high speed
internet connection is 30%
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 A random sample of 12 students was
selected to test the claims.
SG+ Demo
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Binomial Distribution
 A flight is counted as "on time" if it arrived at the gate no more
than 15 minutes after the scheduled arrival time. (Bureau of
Transportation Statistics)
 “United Airlines Beats Four Single-Day On-Time Records as
Superb Operating Performance Continues” (Press release on
3/2003)
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Arrival performance “within 14” (early, on time or within
14 minutes of scheduled arrival) at 96.4 percent.
 Q1. If its performance continues, how likely will you observe 2
late arrivals in the next 5 flights?
 Q2. If 2 late arrivals are observed in the next 5 flights, do you
believe that UA still operates at the record performance?
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Review Question: Warranty Level
Mean = 30,000 miles STD = 5,000 miles
Q1: If the level of warranty is set at 15,000 miles, about what % of tires will be returned
under the warranty?
Q2: If we can accept that up to 2.5% of tires can be returned under warranty, what should be
the warranty level?
0.04
0.03
0.02
0.01
0
0
10
20
30
40
50
60
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The Empirical Rule is not Enough
Mean = 30,000 miles STD = 5,000 miles
Q1: If the level of warranty is set at 12,000 miles, about what % of tires will be returned
under the warranty?
Q2: If we can accept that up to 3% of tires can be returned under warranty, what should be
the warranty level?
0.04
0.03
0.02
0.01
0
0
10
20
30
40
50
60
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The Normal Probability Distribution
 A specific curve that is symmetric and bell-shaped with two
parameters m and s2.
 It has been used to describe variables that are too cumbersome
to be consider as discrete (i.e., continuous variable). For
example,
 Physical measurements of members of a biological
population (e.g., heights and weights), IQ and exam scores,
amounts of rainfall, scientific measurements, etc.
 It can be used to describe the outcome of a binomial experiment
when the number of trials is large.
 It is the foundation of classical statistics.
 Central Limit Theorem
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Notation (p.10)
 X ~ N(m, s2)
 P( X < a ) = P( X ≤ a )
 P( X > b ) = P( X ≥ b )
 P( a < X < b ) = P( a ≤ X < b ) = P( a < X ≤ b )
= P( a ≤ X ≤ b )
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Normal Curve Table (p.40)
© 2003 Brooks/Cole Publishing / Thomson Learning™
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Example 1 (p.11)
m =0
s=1
a = 1.96
A
Prob = ???
a
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Example 2 (p.11)
B
m=0
s=1
a = 1.00
b = 2.00
Prob = ???
a
b
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Example 3 (p.11)
C
m=0
s=1
a = ?????
Prob = 0.0793
a
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Example 4 (p.11)
D
m=0
s=2
a = 2.00
b = ??????
Prob = 0.1005
a
b
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Example 5 (p.11)
E
-0.72
m=2
s=1
Prob = ???
0.34
3.23
4.55
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Example 6 (p.11)
m = -3
s=2
Prob = ???
F
-5.48
-2.56
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