Focus Points
Compute the probability of standardized
events.
Find a z score from a given normal probability
(inverse normal).
Use the inverse normal to solve guarantee
problems.
3
Normal Distribution Areas
4
Normal Distribution Areas
In many applied situa

Focus Points
Given and , convert raw data to z scores.
Given and , convert z scores to raw data.
Graph the standard normal distribution, and find
areas under the standard normal curve.
3
z Scores and Raw Scores
4
z Scores and Raw Scores
Normal distributio

Graphs of Normal Probability Distributions
One of the most important examples of a continuous
probability distribution is the normal distribution.
This distribution was studied by the French mathematician
Abraham de Moivre (16671754) and later by the Germ

Introduction
For instance, if we want to do a study about the people who
have climbed Mt. Everest, then the individuals in the study
are all people who have actually made it to the summit.
1
Introduction
One variable might be the height of such individual

How to describe the distribution:
- Frequency/Relative frequency of data/Percentile
- Measures of central tendency
(Where is the middle of the data?)
- Measures of dispersion
(How dispersed is data?)
Frequency Tables
2
Definition: For each possible value

Measures of Variation
An average is an attempt to summarize a set of data using
just one number. As some of our examples have shown, an
average taken by itself may not always be very meaningful.
We need a statistical cross-reference that measures the
spre

Focus Points
Review such commonly used terms as random
sample, relative frequency, parameter, statistic,
and sampling distribution.
From raw data, construct a relative frequency
distribution for values and compare the result
to a theoretical sampling dist

Focus Points
Compute mean, median, and mode from raw
data.
Interpret what mean, median, and mode tell you.
Explain how mean, median, and mode can be
affected by extreme data values.
What is a trimmed mean? How do you compute
it?
Compute a weighted average

Percentiles and Box-and-Whisker Plots
Weve seen measures of central tendency and spread for a
set of data. The arithmetic mean x and the standard
deviation s will be very useful in later work.
However, because they each utilize every data value, they
can

Binomial Experiment
4
Focus Points
List the defining features of a binomial
experiment.
Compute binomial probabilities using the
formula P (r) = Cn,r prqn r
Use the binomial table to find P (r).
Use the binomial probability distribution to solve
real-worl

Graphing a Binomial Distribution
4
Focus Points
Make histograms for binomial distributions.
Compute and for a binomial distribution.
Compute the minimum number of trials n
needed to achieve a given probability of success
P (r).
3
Graphing a Binomial Distr