Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 12

Normal Distributions

Do most healthy adults have a healthy body temperature close to 98.6 degrees? What proportion of newborn babies are considered to be of low birth weight? If you observe a footprint at the scene of a crime and predict the gender of the criminal based on the length of the footprint, how often will your prediction be incorrect? These are some of the questions that can be addressed with the most important probability distribution in all of statistics: the normal distribution.

Overview

You began your formal study of randomness and probability in the previous topic. Toward the end of that topic, you learned that mound-shaped distributions often model the outcomes of different variables, such as counts and proportions. Such a pattern arises so frequently that it has been extensively studied mathematically. In this topic, you will investigate the mathematical models known as normal distributions, which describe this symmetric pattern of variation very accurately. You will learn how to use normal distributions to calculate probabilities in a variety of contexts.

Preliminaries

1. How much do you think a typical baby weighs at birth? (Activity 12-2)
2. Approximately what proportion of babies would you guess weigh less than 6 pounds? Greater than 10 pounds? (Activity 12-2)
3. Let's say the distribution of men's foot lengths has a mean of 25 centimeters (cm) and a standard deviation of 4 cm, whereas the distribution of women's foot lengths has a mean of 19 cm and a standard ...