1. INTRODUCTORY STATISTICS Chapter 7 THE CENTRAL LIMIT THEOREM PowerPoint Image Slideshow

2. SEC. 7.2: THE CENTRAL LIMIT THEOREM FOR AVERAGES Not every distribution is normal… How do we make a normal distribution from a situation that isn’t necessarily? Use the Central Limit Theorem! This says that if we keep drawing samples and taking their mean, the means will form their own normal distribution, even if the original data was not normal.

3. EXAMPLE

4. MEAN AND STANDARD DEVIATION

5. STANDARD DEVIATION OF SAMPLE MEANS

6. EXAMPLE:

7. PRACTICE

8. ANOTHER EXAMPLE

9. ONE MORE PRACTICE

10. SEC. 7.3: CENTRAL LIMIT THEOREM FOR SUMS The Central Limit Theorem also applies to sums of samples. No matter the type of distribution, if you keep drawing larger and larger samples and taking their sums, the sums form their own normal distribution (the sampling distribution), which approaches a normal distribution as the sample size increases.

11. MEAN AND STANDARD DEVIATION

12. EXAMPLE

13. PRACTICE

14. SEC. 7.4: USING THE CENTRAL LIMIT THEOREM It is important for you to understand when to use the central limit theorem (clt). If you are being asked to find the probability of the mean, use the clt for the mean. If you are being asked to find the probability of a sum or total, use the clt for sums. If you are being asked to find the probability of an individual value, do not use the clt. Use the distribution of its random variable.

15. LAW OF LARGE NUMBERS

16. EXAMPLE In an upcoming election, it is determined that 55% of voters favor a certain bill. There are 1000 voters. a)What is X in words? b)Write the distribution of X. c)What is the probability that 590 voters will vote yes? d)What is the probability that only 450 voters will vote yes?

17. ONE LAST EXAMPLE