Section 4.4
Sampling Distribution Models
and the Central Limit Theorem
Transition from Data Analysis and
Probability to Statistics
Probability:
From population to
sample (deduction)
Statistics:
From sample to the
population (induction)
Sampling Distribut
4.3 NORMAL PROBABILITY
DISTRIBUTIONS
The Most Important Probability
Distribution in Statistics
Normal Distributions
A random variable X with mean and
standard deviation is normally distributed if
its probability density function is given by
2
xx
( / )
4.2 (cont.) Expected Value of
a Discrete Random Variable
A measure of the middle of
the values of a random
variable
Probability
Center
.40
.35
.30
.25
.20
.15
Lousy
Good
OK
Great
.10
.05
-4
-2
0
2
4
6
8
10
12
Profit
The mean of the probability
distributio
Lecture Unit 3
Sample Surveys
Producing Valid Data
If you dont believe in random sampling,
the next time you have a blood test tell the
doctor to take it all.
The election of 1948
The Predictions
The Candidates Crossley Gallup Roper The Results
Truman
45
Binomial Random
Variables
Binomial Probability Distributions
Binomial Random
Variables
Through
2/25/2014 NC States freethrow percentage is 65.1% (315th out
351 in Div. 1).
If in the 2/26/2014 game with UNC,
NCSU shoots 11 free-throws, what is the
probabil
The
Poisson Probability
Models
Poisson experiment typically
models situations where rare
events occur over a fixed amount
of time or within a specified region
Examples
The number of cellphone calls per
minute arriving at a cellphone tower.
The number of
Unit 4 Probability Basics
Laws of Probability
Odds and Probability
Probability Trees
Birthday Problem
What is the smallest number of
people you need in a group so that
the probability of 2 or more people
having the same birthday is greater
than 1/2?
Section 4.1 (cont.) Probability
Trees
A Graphical Method for
Complicated Probability
Problems
Example: Southwest Energy
A Southwest Energy Company pipeline has 3
safety shutoff valves in case the line starts to leak.
The valves are designed to operate i
ODDS AND PROBABILITIES
World Series Odds
From probability to odds
From odds to probability
From Probability to Odds
If event A has
probability P(A),
then the odds in
favor of A are P(A)
to 1-P(A). It
follows that the
odds against A are
1-P(A) to P(A)
If
2.4 Describing Distributions
Numerically cont.
Describing Symmetric Data
1
Symmetric Data
Body temp. of 93 adults
2
Recall: 2 characteristics of a
data set to measure
center
measures where the middle of the
data is located
variability
measures how spread
Lecture Unit 2
Graphical and Numerical
Summaries of Data
UNIT OBJECTIVES
At the conclusion of this unit you should be able to:
1) Construct graphs that appropriately describe data
2) Calculate and interpret numerical summaries of a
data set.
3) Combine nu
Lecture Unit 1
Stats Starts Here
Objectives: be able to
Identify the Who, What, Why, When, Where
and How associated with data
Identify different types of data variables
Statistics: An Overview
Everyday
experiences:
Gallup polls, newspaper articles, lo
The Program
Push A:
Flat Bench
5 sets of 5 reps at 85% of your 1 rep max
Incline Dumbell Press
5 sets of 5 reps at 85% of your one rep max
Standing Military Press
5 sets of 5 reps at 85% of your one rep max
Seated Arnold press
3 sets of 5, 6, 8 reps
Weigh