1. Get out your Normal Curve WS! You will be able to standardize a Normal distribution. Today’s Objectives:

2. Warm Up Take a 3x5 Card from the front table and clear your desk of everything but a pencil. From memory, draw the Normal curve including all %’s inside the curve and the standard deviations underneath the curve. 13.5% 34% 13.5% 2.4%.1%

3. Homework Check

5. Measurement Activity The big idea of this activity is that repeated measurements of the same quantity tend to follow a Normal distribution. You will produce your own data that will be displayed as a dot plot.

6. Measurement Activity 1. Describe the shape, center, and spread of the distribution of measurements. Are there any outliers? 2. Calculate the average textbook length measurement for your class. Compare with the value provided by your teacher. Class Average: _________ Diener Value: _________

7. Z-Scores

8. Z-Score

9. Any time you are asked to standardize a Normal curve you must use the new equation using the new symbols,

10. New symbols—Same meaning

11. Standard Normal Distribution

12. The standard Normal distribution is the Normal distribution with mean 0 and standard deviation 1.

13. Analyze

14. Standard Normal Table All Normal distributions are the same when we standardize. Therefore we can find areas under any Normal curve from a table of values. Turn to the back of your book—Table A.

15. Standard Normal Table Table A is a table of areas under the standard Normal curve.

16. Example 1 Find the proportion of observations from the standard Normal distributions that are (a)Less than -1.25

17. Example 2 Find the proportion of observations from the standard Normal distributions that are (b) Greater than 0.81

18. CAUTION! A common mistake is to look up a z-value in Table A and report the entry corresponding to that z-value, regardless of whether the problem asks for the area to the left or to the right of that z-value! The table give you the area to the LEFT

19. Example 3 Find the proportion of observations from the standard Normal distribution that are between -1.25 and 0.81.

20. How to Solve From Table A, the area to the left of 0.81 is 0.7910 and the area to the left of -1.25 is 0.1056. So just subtract the values to find the answer. 0.81-1.25 0.81 -1.25

21. Practice Questions

22. You Try!

23. Practice Questions

24. You Try!

25. Practice Questions-Backwards

26. You Try!

27. Homework Normal Distribution Worksheet Due Wednesday