1. Chapter 5 The Normal Curve

2. Histogram of Unemployment rates, States database

3. Histogram of Abortion Rates, States Database

4. Histogram of population growth rates from Nations database

5. Histogram of suicide rates from Nations Study

6. Theoretical Normal Curve  Bell Shaped  Unimodal  Symmetrical  Unskewed  Mode, Median, and Mean are same value

7. Theoretical Normal Curve  Distances on horizontal axis always cut off the same area. We can use this property to describe areas above or below any point

8. Theoretical Normal Curve  General relationships: ±1 s = about 68% ±2 s = about 95% ±3 s = about 99%

9. Theoretical Normal Curve

10. Unemployment rates again Mean=3.9%, s=.95  3.9+/-.95 gives a range of 2.95-4.85, which includes 34 states  3.9+/-1.9 gives a range of 2.0-5.8, which includes 29 states

11. Using the Normal Curve: Z Scores  To find areas, first compute Z scores.  The formula changes a “raw” score (X i ) to a standardized score (Z).

12. Using Appendix A to Find Areas Below a Score  Appendix A can be used to find the areas above and below a score.  First compute the Z score, taking careful note of the sign of the score.  Draw a picture of the normal curve and shade in the area in which you are interested.

13. Using Appendix A  Appendix A has three columns. (a) = Z scores. (b) = areas between the score and the mean

14. Using Appendix A  Appendix A has three columns. ( c) = areas beyond the Z score

15. Using Appendix A  Find your Z score in Column A.  To find area below a positive score: Add column b area to.50.  To find area above a positive score Look in column c. (a)(b)(c)... 1.660.45150.0485 1.670.45250.0475 1.680.45350.0465...

16. Using Appendix A  The area below Z = 1.67 is 0.4525 + 0.5000 or 0.9525.  Areas can be expressed as percentages: 0.9525 = 95.25%

17. Normal curve w z=1.67

18. Using Appendix A  What if the Z score is negative (– 1.67)?  To find area below a negative score: Look in column c.  To find area above a negative score Add column b.50 (a)(b)(c)... 1.660.45150.0485 1.670.45250.0475 1.680.45350.0465...

19. Using Appendix A  The area below Z = - 1.67 is 0.475.  Areas can be expressed as %: 4.75%.

20. Finding Probabilities  Areas under the curve can also be expressed as probabilities.  Probabilities are proportions and range from 0.00 to 1.00.  The higher the value, the greater the probability (the more likely the event).

21. Finding Probabilities  If A distribution has: = 13 s = 4  What is the probability of randomly selecting a score of 19 or more?

22. Finding Probabilities 1.Find the Z score. 2.For X i = 19, Z = 1.50. 3.Find area above in column c. 4.Probability is 0.0668 or 0.07. (a)(b)(c)... 1.490.43190.0681 1.500.43320.0668 1.510.43450.0655...