Normal Distribution

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
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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(Y75)
7
P(Ygt50)
8
P(Ylt40)
9
P(40Y60)
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?

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Upper Tail Percentiles (gt50)
Look up a1-p in body of Z-table, obtain zpza
from the edge of table
12
Lower Tail Percentiles (lt50)
Look up ap in body of Z-table, obtain zp-za
from the edge of table
13
90th-Percentile
14
5th-Percentile
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