Transcript Chapter 5 - s3.amazonaws.com

Probability
Chapter 6 (part 4)
4. Example:
It is known that IQ scores form a normal
distribution with μ=100 and σ=15. What is
the probability of randomly selecting an
individual with an IQ score less than 130?
4. Example Contd.
Given μ=100 and σ=15 what is p (X<130)=?
First Step: Sketch the distribution and locate the score and the shade the
area you are interested in.
Second Step: Change X value to Z score. z=(X-μ)/σ = (130-100)/15 = +2.00
Third Step: Look up z-score value in Unit Normal table for are of interest, in
this case the body, z score of +2.00 corresponds to a proportion of
0.9772 so:
p (X<130)=0.9772 (or 97.72%)
5. Looking ahead to Inferential
Statistics
A diagram of a research study. A sample is selected from the
population and receives a treatment. The goal is to determine
whether or not the treatment has an effect.
5. Looking ahead to Inferential
Statistics
Boundaries
provide the
deciding
criteria.
Boundaries
provide the
deciding
criteria.
Using probability to evaluate a treatment effect. Values that are extremely
unlikely to be obtained from the original population are viewed as evidence
of a treatment effect.
Class Exercise-1
If a vertical line is drawn through a normal
distribution at each of the following zscore locations, then determine whether
the tail is on the left side or the right side
of the line and determine what proportion
of the distribution is located in the tail:
z=+1.00, z=+0.50, z=-1.50, z=-2.00
Class Exercise-2
For a normal distribution, find the z-score location
of a line that would separate the distribution as
described in each of the following:
a. Where should the line be drawn to separate
the top 5% from the rest?
b. Where should the line be drawn to separate
the top 20% from the rest?
c. Where should the line be drawn to separate
the bottom 40% from the rest?
Class Exercise-3
A normal distribution has a mean of μ=61
with a σ=8. Find the following
probabilities:
a. p (X<55)
b. p (X<70)
c. p (51<X<73)