Download PPSection 2.2C

AP Statistics: 5E Section 2.2 C
Example 1: Determine if each of the
following is likely to have a Normal
distribution (N) or a non-normal
distribution (nn).
N gas mileage of 2006 Corvettes
_____
_____
nn prices of homes in Westlake
_____
nn gross sales of business firms
_____
N weights of 9-oz bags of potato chips
While experience can suggest whether or
not a Normal distribution is plausible in a
certain case, it is very risky (especially on
the AP test) to assume that a distribution is
Normal without actually inspecting the
data. Chapters 8 -10 of our text deal with
inference, and an important condition that
will need to be met is that the data comes
from a population that is approximately
Normal.
Method 1: Construct a histogram,
stemplot or dotplot.
What are we looking for?
bell - shaped and symmetrical
Non-Normal features to look for
include ________,
pronounced
outliers
skewness
gaps and
_________,
or ______
clusters
________.
If we had a box-and-whisker plot (i.e. the
5-number summary) what are we looking
for?
Most importantly, we are looking for the boxplot
to be roughly symmetrical. Then we would like to
see the box tightly grouped around the center while
the whiskers are slightly longer.
Note: What should be true about
the mean and the median in a
Normal distribution?
Since a Normal distribution is symmetrical, the mean
and median should be approximately equal
To be truly Normal, such a bellshaped plot should conform to the
68-95-99.7 rule. Mark the points
on the horizontal axis and
determine the percentage of
counts in each interval.
1s from x : 649
947
2s from x : 903
3s from x : 945
 68.5%
947
947
 95.4%
 99.8%
YES
Method 3: Construct a Normal
probability plot. Statistical packages,
as well as TI calculators, can construct
a Normal probability plot. Before we
look at constructing a Normal
probability plot, let’s look at some
basic ideas behind constructing a
Normal probability plot.
1. Arrange the observed data
values from _________
smallest to
_________.
largest
th
5
Record what percentile of the data
each value represents.
2. Determine the z-scores for each
of the observations. For example,
z = _______
1.645 is the 5% point of the
standard Normal distribution and
z = _______
 1.28 is the 10% point.
3. Plot each data point x against
the corresponding z. If the data
distribution is close to Normal, the
plotted points will be
__________________.
approximately linear
Systematic deviations from a
straight line indicate a non-Normal
distribution.
In a right-skewed distribution, the
largest observations fall distinctly
to the right of line drawn through
______________a
the main body of points. In a leftskewed distribution, the smallest
observations fall distinctly
____________
to the left of a line drawn through
the main body of points
Construct a Normal probability plot on your
calculator as follows:
1. Enter the data in L1. (STATS, EDIT).
2. Go to STAT PLOT (2nd Y=). ENTER. Highlight ON.
First draw a histogram to see that the data
appears to be Normally distributed. Key ZOOM 9
to get an appropriate window.
3. Go back to STAT PLOT. Change “Type” to the 6th
graph choice. For “Data List”, put in L1 and
for “Data Axis”, highlight Y.
4. Push GRAPH and key ZOOM 9 to get an
appropriate window.
Do not worry too much about
small deviations from the linear
pattern at the ends of the
distribution. When a distribution is
skewed, there will be noticeable
bend in the plot.
MATH
PRB
6 : RandNorm
The data is
approximately
Normally
distributed
The data is
right - skewed
Note that the values to the right of the line are
much larger values then expected based on the
corresponding z - scores from the standard Normal
distribution which is indicated by the line.