6–1
Objectives
After completing this chapter, you should be able to
1
Identify distributions as symmetric or skewed.
2
Identify the properties of a normal distribution.
3
Find the area under the standard normal
distribution, given various
z
values.
4
Find probabilities for a normally distributed
variable by transforming it into a standard
normal variable.
5
Find specific data values for given
percentages, using the standard normal
distribution.
6
Use the central limit theorem to solve
problems involving sample means for large
samples.
7
Use the normal approximation to compute
probabilities for a binomial variable.
Outline
6–1
Introduction
6–2
Properties of a Normal Distribution
6–3
The Standard Normal Distribution
6–4
Applications of the Normal Distribution
6–5
The Central Limit Theorem
6–6
The Normal Approximation to the Binomial
Distribution
6–7
Summary
6
6
The Normal
Distribution
C
H
A
P
T
E
R
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Chapter 6
The Normal Distribution
6–2
Statistics
Today
What Is Normal?
Medical researchers have determined socalled normal intervals for a person’s blood
pressure, cholesterol, triglycerides, and the like. For example, the normal range of sys
tolic blood pressure is 110 to 140. The normal interval for a person’s triglycerides is from
30 to 200 milligrams per deciliter (mg/dl). By measuring these variables, a physician can
determine if a patient’s vital statistics are within the normal interval or if some type of
treatment is needed to correct a condition and avoid future illnesses. The question then is,
How does one determine the socalled normal intervals? See Statistics Today—Revisited
at the end of the chapter.
In this chapter, you will learn how researchers determine normal intervals for specific
medical tests by using a normal distribution. You will see how the same methods are used
to determine the lifetimes of batteries, the strength of ropes, and many other traits.
6–1
Introduction
Random variables can be either discrete or continuous. Discrete variables and their dis
tributions were explained in Chapter 5. Recall that a discrete variable cannot assume all
values between any two given values of the variables. On the other hand, a continuous
variable can assume all values between any two given values of the variables. Examples
of continuous variables are the heights of adult men, body temperatures of rats, and cho
lesterol levels of adults. Many continuous variables, such as the examples just mentioned,
have distributions that are bellshaped, and these are called
approximately normally dis
tributed variables.
For example, if a researcher selects a random sample of 100 adult
women, measures their heights, and constructs a histogram, the researcher gets a graph
similar to the one shown in Figure 6–1(a). Now, if the researcher increases the sample size
and decreases the width of the classes, the histograms will look like the ones shown in
Figure 6–1(b) and (c). Finally, if it were possible to measure exactly the heights of all
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 Spring '09
 Soshiani
 Normal Distribution, researcher, Theoretical Normal Distribution

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