Binomial and Poisson Probability Distributions

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CHAPTER 5

• Binomial and Poisson Probability Distributions

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The Poisson Distribution

• Discrete
• Probability
• Distribution
• Binomial Distribution

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Example 1

• Suppose you take a 25 question multiple choice
  test where each question has 5 choices. This is
  the pop quiz from Hades that you had no clue was
  coming and have no clue as to the correct
  answers, so you randomly guess at each question.

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• Is the scenario binomial
• Find the probability that you guess correctly at
  exactly 15 questions.
• Find the probability that you get at most 8
  correct answers.
• Find the probability that you get at least 12
  correct.

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The Poisson Distribution

• Properties
• The PDF P(x)

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Example 2

• During a period of time phone-in registrations
  are taken at BCCC at the rate of one call every 2
  minutes.
• a) find the expected number of calls in one hour
• b) find the probability of having 3 calls in a
  5-minute period

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• c) find the probability of at most 2 calls in 5
  minutes
• d) find the probability of more than one call in
  5 minutes

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Example 3

• Each year 450 accidental deaths due to firearms
  occur in the 15-24 age group
• a) find the average number of accidental deaths
  due to firearms in a typical week
• b) find the probability of no accidental deaths
  due to firearms in a typical week
• c) find the probability of 2 or more accidental
  deaths due to firearms in a typical day

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Example 4

• Household Information and Security Systems
  produces and installs 300 custom made home
  security units every week. The units are priced
  to include a one-day installation. A unit with
  either a design or production problem must be
  modified on site and will require more than 1 day
  to install. After an intensive self study of
  their records, HISS has found that if they are
  operating at standard quality, 10 of the units
  will have problems and require a second day to
  install. For quality control HISS samples 6
  systems and records the number with problems.
  Find the probability that the number of security
  systems (out of 6) that require a second day of
  service will be

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• A) none
• B) at most 1
• C) less than 3