1. Normal Distribution Percent Voting for G.W. Bush among U.S. Counties – 2004 Makes use of Z-Tables with upper-tail probabilities (1-F(z))

2. Data Percent Voting for G.W. Bush (among those voting for Bush, Kerry, Nader) 3109 Counties/Cities in Conterminous U.S. (Note: Virginia has several “independent cities”, St. Louis, Baltimore

3. Descriptive Statistics

5. Problems Involving Probabilities Y ~ N(60.7,12.6) Approximately Probability that a randomly selected county has at least 75% Vote for GWB? That a Majority favors GWB? That fewer than 40% favor GWB? Between 40 and 60% favor GWB?

6. P(Y≥75)

7. P(Y>50)

8. P(Y<40)

9. P(40≤Y≤60)

10. Problems Involving Percentiles Y ~ N(60.7,12.6) Approximately Above what percentage do the highest 10% fall? Below what percentage do the lowest 5% fall? Between what percentages do the middle 50% fall?

11. Upper Tail Percentiles (>50%) Look up a=1-p in “body” of Z-table, obtain z p =z a from the “edge” of table

12. Lower Tail Percentiles (<50%) Look up a=p in “body” of Z-table, obtain z p =-z a from the “edge” of table

13. 90 th -Percentile z.07.08.09 1.1.1210.1190.1170 1.2.1020.1003.0985 1.3.0853.0838.0823

14. 5 th -Percentile z.04.05 1.5.0618.0606 1.6.0505.0495 1.7.0409.0401