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The Central Limit Theorem (Lesson 7.5)

Chapter 7 - Day 6

Learning Targets
  • Determine if the sampling distribution of x-bar is approximately normal when sampling from a non-normal population.

  • If appropriate, use a normal distribution to calculate probabilities involving x-bar.

Activity: How Tall to be in the NBA? Part 2
NBA Gaurds Height Data

Experience First

This lesson uses a similar context to the previous lesson, except that here we are looking at the distribution of height for NBA shooting guards rather than the distribution of height for NBA power forwards. Notice that the population distribution here is NOT approximately normal -- it is skewed left. 

Once again, there is an extra handout that you will need to make copies of or display during the lesson. Also, you will need to prepare two posters for a dotplot (expect values between 74 inches and 79 inches) and students will need sticker dots. Use the same scale for each of the dotplots so that students will clearly see the variability of the sampling distribution decreases as the sample size increases.

Formalize Later

Be sure to point out that the first sampling distribution with n = 2 still has a shape that is similar to the shape of the population distribution (skewed left). It is only when we increase our sample size to n = 10 that the population distribution really starts to show an approximately normal distribution. To be extra safe, we will use n >= 30 as our benchmark to guarantee the sampling distribution is approximately normal.

If you have a small class and are worried that your dotplots will not have enough dots to reveal shape, you can use this StatKey applet, which allows you to upload the population data and then create sampling distributions with different sample sizes. 

Consider using this applet as an extra demonstration of the Central Limit Theorem. With this applet you can create a "Custom" population distribution with any shape you can come up with. The applet shows that if the sample size is large enough, the sampling distribution of the sample means will be approximately normal. 

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