Lesson 7: Common Distributions

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Lesson 7 Learning Objectives

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

  • find the area under a normal distribution using Minitab Express and StatKey.
  • compute a test statistic for a normally distributed sampling distribution. 
  • construct a confidence interval at any level of confidence using a normally distributed sampling distribution.
  • compute the mean and standard deviation of a binomial distribution. 
  • find probabilities associated with a binomial distribution using Minitab Express.

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 distribution for a proportion  Bootstrap distribution for a single mean   Bootstrap distribution for a correlation   Randomization distribution for difference in means 

These four distributions are all approximately normally distributed. You were first introduced to the normal distribution in Lesson 2 as a special type of symmetrical distribution also known as a "bell-shaped" distribution.

In this lesson we will learn about how many sampling distributions can be approximated using a normal distribution. At the end of this lesson you will also be introduced to the binomial distribution which can also be used to approximate some sampling distributions for proportions when sample sizes are smaller.