Raul CruzCano

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Lecture 17 Section 5.4 Distribution of the
Sample Proportion

• Raul Cruz-Cano
• Math 453 Fall 2008
• Texas AM-Texarkana

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Announcements

• Review before Exam 2 Thursday, October 6th
• Exam 2 Tuesday October 11th
• Tuesday October 25th I might not be here

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Sample Proportion

• There are populations in which the units can have
  many different values
• Age18,19,21,23,
• There populations in which each element can be
  considered a success or failure
• Male?1,1,0,1,0,0,...
• Let p be the proportion of success in the
  population.

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The variable of interest is the Sample Proportion
(unknown mean, unknown standard deviation)
Use population proportion to find the mean and
standard deviation of the sample proportion
Normal Distribution Function (Variable of
interest has known mean, known standard deviation)
Unknown Value Problems
Unknown Percentage Problems
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Distribution of the Sample Proportion

• Regardless of the value of p the Distribution of
  the number of success in sample is

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Example

• TAMU-T football team has (historically) a winning
  percentage of 83.
• The 2008 season consist of 12 games
• What is the probability that they do not have a
  winning season (6-6 or worse)?
• What is the probability that they have bowl
  eligibility (7-5 or better)?
• How many games they have to win to be considered
  for the TAMU-T Hall of Fame (top 10)?

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Probabilities of Sample Proportion
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Probabilities of Sample Proportion

• Mean9.96
• Standard Deviation 1.3
• Probability that the team win 6 games or less?
  (Unknown Percentage Problem, less than)

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Probabilities of Sample Proportion

• Mean9.96
• Standard Deviation 1.3
• Probability that the we win 7 games or more?
• (Unknown Percentage Problem, above than)

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Example
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Examples

• E. 22, page 300 a,b,c (Average)
• E. 24, page 300 (Average)
• E. 26 page 300 (Total)
• E. 31 page 310 (Proportion)
• E. 32 page 310 (Proportion)
• E. 40 page 319 (Total)
• E. 48, page 323 (Average)