Berry

132 Chapter 5
A QUESTION OF TERMINOLOGY
One very important idea in statistics is the idea of a distribution. For a discrete
variable, a distribution is a lot like a histogram—it tells how often a given value
occurs as a probability between 0 and 1. For instance, a uniform distribution
says that all values are equally represented. An example of a uniform
distribution would occur in a business where customers pay by credit card
and the same number of customers pays with American Express, Visa, and
MasterCard.
The normal distribution, which plays a very special role in statistics, is an
example of a distribution for a continuous variable. The following figure shows
the normal (sometimes called Gaussian or bell-shaped) distribution with a
mean of 0 and a standard deviation of 1. The way to read this curve is to
look at areas between two points. For a value that follows the normal
distribution, the probability that the value falls between two values—for
example, between 0 and 1—is the area under the curve. For the values of 0
and 1, the probability is 34.1 percent; this means that 34.1 percent of the time
a variable that follows a normal distribution will take on a value within one
standard deviation above the mean. Because the curve is symmetric, there is
an additional 34.1% probability of being one standard deviation below the
mean, and hence 68.2% probability of being within one standard deviation
above the mean.
40%
35%
TEAMFLY
Probability Density
30%
25%
20%
15%
10%
5%
0%
-5 -4 -3 -2 -1 0 1 2 3 4 5
Z-Value
The probability density function for the normal distribution looks like the familiar
bell-shaped curve.
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