1)
B: the event that a car fails an emissions test within two years.
A1: The event that a car has small engine
A2: The event that a car has medium-size engine
A3: The event that a car has large engine
P(A1)=0.40
P(A2)=0.40
P(A3)=0.20
Given P(B|A1)=0.10, P

Binomial (section 4.6)
RV of interest, Y = total # of successes
Follows directly from Bernoulli distribution
A series of n Bernoulli trials
0 < p(y) < 1
p(y) = 1
Probability distribution of Y can be presented as a table, graph or formula
Binomial Distri

Random Variables and Discrete Probability Distributions
Chapter 4
Sections: 4.1-4.6; 4.8 - 4.10
Definition
Random Variable: A function that assigns a numeric value to every possible outcome
Flipping a coin 5 times and using random variable X to denote the

Empirical Rule and Law of Large Numbers
a) Single observation will be within two or three standard deviations of mean (Empirical
Rule)
b) Average of a large number of repetitions of same experiment will be close to
expected value
Example 4.6 page 125
Calc

Descriptive Statistics
Chapter 2.1 - 2.8
Statistics
The science of:
Collecting data,
Analyzing,
Presenting
Making conclusions
Statistics
Definition
Qualitative
Measurement with words
Quantitative
Measurement with numbers
Product Quality in the US before

Addendum:
Graphing Data
Lets start with some common Excel graph types and see how they look with the
random order data.
Here are the default Column Chart and Bar Chart views
What do these graphs tell you?
What does the x-axis represent in the column char

Graphs
Understand data
Analyze Data (qualitative)
Analyze Data (quantitative)
What is a Statistic?
A Statistic - numerical descriptive measure computed from sample data
Characteristics of a Sampling Distribution
Central tendency
median
average/mean
mode

Variance,
Standard Deviation,
Calculator formula
Dispersion: Example
Dispersion: Example
Normal Distribution
Quantifying Normal Distribution
Measures of Relative Standing
1st Quartile
Median (2nd Quartile)
3rd Quartile
xx% Percentile
Finding Quartiles wi

1.
The table above shows sales performance of sales staff of an insurance
company last month. What is the variance of number of sales per employee?
A)
281.5
B) 250.4
C) 222.5
D) 150.4
(For Q2 Q3)
A large industrial firm allows a discount on any invoice th

# of sales
P(x)
100
0.10
90
0.55
80
0.30
70
0.05
1. The table above shows sales performance of sales staff of an insurance company
last month. What is the variance of number of sales per employee?
A) 23
B) 51
C) 65
D) 74
(For Q2 Q3)
A large industrial fir

Chapter 4
Equilibrium: How
Supply and Demand
Determine Prices
MODERN PRINCIPLES OF ECONOMICS
Third Edition
Outline
Equilibrium and the Adjustment Process
A Free Market Maximizes Producer Plus
Consumer Surplus (the Gains from Trade)
Does the Model Work?