Chapter 5 Probability Distributions 189
Because the area under the curve is equal to 0.6827, the probability
of a value falling between 2 1 and 1 is equal to 68.27%. Try experi-
menting with other range boundaries until you get a good feel for
the relationship between probabilities and areas under the curve.
3 Click the left scroll arrow until the left boundary equals 2 3.
4 Click the right scroll arrow until the right boundary equals 3.
Note that when you move the lower boundary to 2 3 and the upper
boundary to 3, the probability is 99.73%, not 100%. That is because
this particular probability distribution extends from minus infi nity
to plus infi nity; the area under the curve (and hence the probability)
is never 1 for any fi nite range.
5 Close the Probability workbook. You do not have to save any changes.
Random Variables and Random Samples
Values from a discrete or continuous probability distribution function
are manifested in a random variable where a random variable is a vari-
able whose values occur at random, following a probability distribution.
A discrete random variable comes from a discrete probability distribution,
Figure 5-5
Selecting
the range
from -1 to 1
