Page 159 - Statistics for Dummies

Chapter 9
The Normal Distribution
In This Chapter
▶ Understanding the normal and standard normal distributions
▶ Going from start to finish when finding normal probabilities
▶ Working backward to find percentiles
n your statistical travels you’ll come across two major types of random
Ivariables: discrete and continuous. Discrete random variables basically
count things (number of heads on 10 coin flips, number of female Democrats
in a sample, and so on). The most well-known discrete random variable is the
binomial. (See Chapter 8 for more on discrete random variables and binomi-
als). A continuous random variable is typically based on measurements; it
either takes on an uncountably infinite number of values (values within an
interval on the real line), or it has so many possible values that it may as well
be deemed continuous (for example, time to complete a task, exam scores,
and so on).
In this chapter, you understand and calculate probabilities for the most
famous continuous random variable of all time — the normal distribution.
You also find percentiles for the normal distribution, where you are given a
probability as a percent and you have to find the value of X that’s associated
with it. And you can think how funny it would be to see a statistician wearing
a T-shirt that said “I’d rather be normal.”

Exploring the Basics of the

Normal Distribution

A continuous random variable X has a normal distribution if its values fall
into a smooth (continuous) curve with a bell-shaped pattern. Each normal
distribution has its own mean, denoted by the Greek letter μ (say “mu”); and
its own standard deviation, denoted by the Greek letter σ (say “sigma”). But
no matter what their means and standard deviations are, all normal distribu-
tions have the same basic bell shape. Figure 9-1 shows some examples of
normal distributions.

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