Computational Thinking in Science and Math

The Central Limit Theorem

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By the end of this lesson, you should be able to:

• Explain how the shape of the sampling distribution of  is affected by the shape of the population distribution and the sample size (aka, The Central Limit Theorem)
• Explain why the Central Limit Theorem is one of the fundamental theorems in statistics
• Calculate the mean and standard deviation of the sampling distribution of a sample mean \(\bar x\) and interpret the standard deviation
• Calculate the mean and standard deviation of the sampling distribution of a difference in sample means \(\bar x_1- \bar x_2\) and interpret the standard deviation
• Determine if the sampling distribution of \(\bar x_1- \bar x_2\) is approximately Normal
• If appropriate, use a Normal distribution to calculate probabilities involving \(\bar x\) and  \(\bar x_1- \bar x_2\)