# 7: Normal Distributions

7: Normal Distributions## Objectives

Upon successful completion of this lesson, you should be able to:

- Describe the standard normal distribution
- Determine the area under a normal distribution using Minitab
- Determine the points that offset a given proportion of a normal distribution using Minitab
- Summarize the Central Limit Theorem
- Conducted a hypothesis test using a standardized test statistic
- Construct a confidence interval using the standard form

Over the last three lessons you have approximated sampling distributions using bootstrapping and randomization methods. You may have noticed that many of the distributions that you constructed had similar shapes, such as those below:

Randomization Dotplot of Proportion

Bootstrap Dotplot of Mean

Bootstrap Dotplot of Correlation

Randomization Dotplot of \(\bar{x}_1-\bar{x}_2\)