Book cover for Fundamentals of Biostatistics

Fundamentals of Biostatistics

Bernard Rosner

ISBN #9781305268920

8th Edition

1,397 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter emphasizes the central role of continuous probability distributions, with a spotlight on the normal distribution. It covers how to utilize the pdf and cdf for computing probabilities and introduces standardizationā€”a technique for transforming any normal distribution into the standard normal for ease of use. Additionally, the chapter discusses approximating discrete distributions such as the binomial and Poisson using the normal distribution under certain conditions. A strong understanding of these principles is essential for performing estimation, hypothesis testing, and various applications in fields ranging from healthcare to manufacturing.

Learning Objectives

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Key Concepts

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Example Problems

Example 1

Because serum cholesterol is related to age and sex, some investigators prefer to express it in terms of $z$ -scores. If $X=$ raw serum cholesterol, then $$Z=\frac{X-\mu}{\sigma}$$, where $\mu$ is the mean and $\sigma$ is the standard deviation of serum cholesterol for a given age-gender group. Suppose $Z$ is regarded as a standard normal random variable. What is $\operatorname{Pr}(Z<0.5) ?$

Example 2

Because serum cholesterol is related to age and sex, some investigators prefer to express it in terms of $z$ -scores. If $X=$ raw serum cholesterol, then $$Z=\frac{X-\mu}{\sigma}$$, where $\mu$ is the mean and $\sigma$ is the standard deviation of serum cholesterol for a given age-gender group. Suppose $Z$ is regarded as a standard normal random variable. What is $\operatorname{Pr}(Z>0.5) ?$

Example 3

Because serum cholesterol is related to age and sex, some investigators prefer to express it in terms of $z$ -scores. If $X=$ raw serum cholesterol, then $$Z=\frac{X-\mu}{\sigma}$$, where $\mu$ is the mean and $\sigma$ is the standard deviation of serum cholesterol for a given age-gender group. Suppose $Z$ is regarded as a standard normal random variable. What is $\operatorname{Pr}(-1.0<Z<1.5) ?$

Example 4

Suppose a person is regarded as having high cholesterol if $Z>2.0$ and borderline cholesterol if $1.5<Z<2.0$. What proportion of people have high cholesterol?

Example 5

Suppose a person is regarded as having high cholesterol if $Z>2.0$ and borderline cholesterol if $1.5<Z<2.0$. What proportion of people have borderline cholesterol?
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