Binomial Probability Distributions

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Section 5-3

• Binomial Probability Distributions

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What does the prefix Bi mean?

• We will now consider situations where there are
  exactly two outcomes
• Yes/no to a survey question
• Product is defective/not defective
• Correct/Wrong response to a multiple choice
  question
• Arrival time for an airline is on time/not on time

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Conditions for a Binomial Probability Distribution

• There are a fixed number of trials, n, that are
  identical and independent.
• Each trial has exactly 2 outcomes success, S
  or failure, F
• The probability of success must remain the same
  for each trial.

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Notation

• P(S) p
• P(F) 1 p q
• n of trials
• x of successes
• success is just what is being measured

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Example 1

• Determine whether the given procedure results in
  a binomial distribution.
• Determining whether each of 3000 heart pacemakers
  is acceptable or defective.
• Surveying people and asking them what they think
  of the current president.
• Spinning the roulette wheel 12 times and finding
  the number of times that the outcome is an odd
  number.

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Methods for finding binomial probabilities

• Binomial Probability Formula
• Table A-1, Appendix A
• MINITAB

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Example 2
A report from the Secretary of Health and Human
Services stated that 70 of single-vehicle
traffic fatalities that occur at night on
weekends involve an intoxicated driver. If a
sample of 10 single-vehicle traffic fatalities
that occur at night on a weekend is selected,
find the probability that exactly seven involve a
driver that is intoxicated.

• This is a binomial experiment where
• n 10 x 7 p 0.70 q 0.30

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• Using table generated in MINITAB

P(7) 0.266828
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• How about the probability of at least 8 involving
  an intoxicated driver?
• P(at least 8) P(8) or P(9) or P(10)
• 0.233474 0.121061 0.028248
• 0.382783

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Example 3

• In a clinical test of the drug Viagra, it was
  found that 4 of those in a placebo group
  experienced headaches.
• Assuming that the same 4 rate applies to those
  taking Viagra, find the probability that among
  eight Viagra users, three experience headaches.

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