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Published byEdith Heath Modified over 6 years ago

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The Central Limit Theorem Today, we will learn a very powerful tool for sampling probabilities and inferential statistics: The Central Limit Theorem

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If samples of size n>29 are drawn from a population with mean,, and standard deviation,, then the sampling distribution of the sampling means is nearly normal and also has mean and a standard deviation Of WTHeck?!!!

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The Central Limit Theorem When working with distributions of samples rather than individuatl data points we use rather than is called the Standard Error

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The Central Limit Theorem Example The average fundraiser at BHS raises a mean of $550 with a standard deviation of $35. Assume a normal distribution: Problem we are used to: What is the probability the next fundraiser will raise more than $600? Sampling problem: What is the probability the next 10 fundraisers will average more than $600

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The Central Limit Theorem The average fundraiser at BHS raises a mean of $550 with a standard deviation of $35. Assume a normal distribution: Problem we are used to: What is the probability the next fundraiser will raise more than $600?

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The Central Limit Theorem The average fundraiser at BHS raises a mean of $550 with a standard deviation of $35. Assume a normal distribution: Sampling problem: What is the probability the next 30 fundraisers will average more than $600

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The Central Limit Theorem This makes sense: It would be much more common for a single fundraiser to vary that much from the mean, but not very likely that you get ten that average that high.

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The Central Limit Theorem Example Two: Mr. Gillam teachers 10,000 students. Their mean grade is 87.5 and the standard deviation is 15. a)What is the probability a group of 35 students has a mean less than 90?

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