Lesson 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 Express
  • Determine the points that offset a given proportion of a normal distribution using Minitab Express
  • 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

Randomization Dotplot of Proportion

 

Bootstrap Dotplot of Mean

Bootstrap Dotplot of Mean

Bootstrap Dotplot of Correlation

Bootstrap Dotplot of Correlation

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

Randomization Dotplot of x(bar)1 - x(bar)2

These are all approximately normally distributed. You were first introduced to the normal distribution in Lesson 2 as a special type of symmetrical distribution. In this lesson, we'll review normal distributions, learn how to use Minitab Express to construct plots of normal distributions, and learn how the Central Limit Theorem allows us to apply what we know about the normal distribution to construct confidence intervals and conduct hypothesis tests without using simulations.