1. Once again, my blog site is www.mathwithdillon.weebly.com www.mathwithdillon.weebly.com You should visit this site to get notes and assignments, check HW and WS, and check the calendar for assessment dates.

2.  Come see me if you don’t understand a concept.  You should bring your worked homework problems so I can see what your mistake is.  You have to attempt homework problems before I can help you. I don’t know how to help you unless I see some work from you.

3. DG5 --- 20 minutes20 minutes

4. Accel Math III Unit #1: Data Analysis Lesson #8: Normal Distribution EQ: What are the characteristics of a normal distribution and how is probability calculated using this type of distribution?

5. Recall: Three Types of Distributions Binomial Normal Geometric Normal Distributions --- created from continuous random variables

6. Characteristics of a Normal Distribution: 1.Symmetric, Bell-Shaped Curve and Uni-modal.

8. 2. Mean, Median, Mode are equal and located at the middle of the distribution. Symmetric about the mean. Not skew.

9. 3. The curve is continuous, no gaps or holes. The curve never touches or crosses the x-axis. 4.The total area under the curve equals 1. Recall: Empirical Rule

10. Normal Distribution --- each has its own mean and standard deviation. What are µ and σ in this normal distribution ? 50 10

11. Standard Normal Distribution --- mean is always 0 and standard deviation is always 1 STANDARDIZE

12. z-score --- the number of standard deviations above or below the mean z = observed – mean or z = X - µ standard deviation σ Correlates to area under the curve.

13. Ex. In a study of bone brittleness, the ages of people at the onset of osteoporosis followed a normal distribution with a mean age of 71 and a standard deviation of 2.8 years. What z-score would an age of 65 represent in this study? 62.6 65.4 68.2 71 73.8 76.6 79.4 | | | -3 -2 -1 0 1 2 3 | 65 | -2.14

14.  Using Table A to Finding the Area under A Standard Normal Curve

15. Ex. Find the area under the curve to the left of z = -2.18. | -2.18

16. Ex. Find the area under the curve to the left of z = 1.35. | 1.35

17. Ex. Find the area under the curve to the right of z = 0.75. |.75 WHY??

18. Ex Find the area under the curve between z = -1.36 and z = 0.42.

19. Ex. Find the area under the curve between z = 1.60 and z = 3.3.

20. In Class Practice Worksheet: Area Under the Standard Normal Curve #1 - 11

21.  What about finding a z-score when given area under the curve? Ex. Determine the z-score that would give this area under the curve.

24. In Class Practice Worksheet: Area Under the Standard Normal Curve #12 Practice Worksheet Calculating Area Using z-scores

25. Quiz 2 --- 30 minutes

26. Using the Graphing Calculator with Normal Distributions Command and Arguments: I.When given a z-score, you are looking for area under the curve. normalcdf(low bound, high bound)

27. Ex. Find the area under the curve to the left of z = 1.35.

28. Ex Find the area under the curve between z = -1.36 and z = 0.42.

29. Assignment: Example Handout: Area Under the Standard Normal Curve #1 – 11 Go back and rework these using the calculator function.

30. II.When given area, you’re looking for a z-score. Use invnorm function under distributions. invnorm(% to the left)

33. ***Remember invnorm and normcdf are calculator jargon Do not write these functions on assessments as “work”. Assignment: Redo WS Calculating Area Using z-scores