Use the information on
page 744
to explain how the heights of professional athletes are distributed. Include a histogram of the given data, and an explanation of whether you think the data is normally distributed.
12-7
The Normal Distribution
12
Main Ideas
. Determine whether
set of data appears to
bermally
distributed or skewed
– Solve problem
involving normally
distributed data
New Vocabulary
discrete probability
பி distribution
continuous probability
distribution
normal distribus
skewed distribution
GET READY for the Lesson
The frequency table below
lists the heights of the 2005
New England Patriots. However, it
does not show how these
heights compare to the
average height of a
professional football player.
To make that comparison,
you can determine how the
heights are distributed
Height .) 70 71 72 73 75 76 77 78 79 20
Frequency 133 5 7
14 2 4
1
Sourcewww..com
Normal and Skewed Distributions The probability distributions you
have studied thus far are discrete probability distributions because they
have only a finite number of possible values. A discrete probability
distribution can be represented by a histogram. For a continuous
probability distribution, the outcome can be any value in an interval
of real numbers. Continuous probability distributions are represented
by curves instead of histograms.
The curve at the right represents a
Normal Dretribution
continuous probability distribution Notice
that the curve is symmetric. Such a curve is
often called a bell cure. Many distributions
with symmetric curves or histograms are
normal distributions
Study Tip
Skewed
Distributions
In a positively siwed
distribution, the long
talis in the positive
direction. These are
Sometimes said to be
skewed to the right in
arregatively swed
distribution, the long
talis in the negative
direction. These are
sometimes said to be
stewed the
A curve or histogram that is not symmetric represents a skewed
distribution. For example, the distribution for a curve that is high at the
left and has a tail to the right is said to be positively skeurd. Similarly, the
distribution for a curve that is high at the right and has a tail to the left is
said to be negatively skewed
Positively skewed
Negatively skewed
724 Chapter 12 Probability and Statistics
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