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

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?!!!

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

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

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?

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

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.

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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