Normal Distribution
blu34978_ch06.qxd
8/13/08
4:39 PM
Page 299
Confirming Pages
C H A P T E
R
6
The Normal
Distribution
Objectives
Outline
After completing this chapter, you should be able to
1
2
3
Identify distributions as symmetric or skewed.
4
Find probabilities for a normally distributed variable by transforming it into a standard normal variable.
Introduction
6–1
Normal Distributions
Identify the properties of a normal distribution.
Find the area under the standard normal distribution, given various z values.
5
Find specific data values for given percentages, using the standard normal distribution. 6
6–3 The Central Limit Theorem
6–4 The Normal Approximation to the Binomial
Distribution
Use the central limit theorem to solve problems involving sample means for large samples. 7
6–2 Applications of the Normal Distribution
Use the normal approximation to compute probabilities for a binomial variable.
Summary
6–1
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Page 300
Confirming Pages
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Chapter 6 The Normal Distribution
Statistics
Today
What Is Normal?
Medical researchers have determined so-called normal intervals for a person’s blood pressure, cholesterol, triglycerides, and the like. For example, the normal range of systolic 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 so-called 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
8/13/08
4:39 PM
Page 299
Confirming Pages
C H A P T E
R
6
The Normal
Distribution
Objectives
Outline
After completing this chapter, you should be able to
1
2
3
Identify distributions as symmetric or skewed.
4
Find probabilities for a normally distributed variable by transforming it into a standard normal variable.
Introduction
6–1
Normal Distributions
Identify the properties of a normal distribution.
Find the area under the standard normal distribution, given various z values.
5
Find specific data values for given percentages, using the standard normal distribution. 6
6–3 The Central Limit Theorem
6–4 The Normal Approximation to the Binomial
Distribution
Use the central limit theorem to solve problems involving sample means for large samples. 7
6–2 Applications of the Normal Distribution
Use the normal approximation to compute probabilities for a binomial variable.
Summary
6–1
blu34978_ch06.qxd
8/13/08
4:39 PM
Page 300
Confirming Pages
300
Chapter 6 The Normal Distribution
Statistics
Today
What Is Normal?
Medical researchers have determined so-called normal intervals for a person’s blood pressure, cholesterol, triglycerides, and the like. For example, the normal range of systolic 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 so-called 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