Poisson distribution

Lessons

• Introduction
  What is the Poisson Distribution?

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• 1.
  Determining the Poisson Distribution
  The number of meteors that hit the earth in a given day is modelled by a Poisson Distribution with $\lambda=4$. What is the probability that 5 meteors hit the earth in a day?

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• 2.
  When making a video I typically make 1 error for every 20 minutes of video time. If I make 45 minutes of video what is the probability that I make 3 errors?

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• 3.
  In a particular community the average person survives to age 100 with probability 0.005 (which is equivalent to 0.5%). If this community has 2,000 people, then what is the probability that 15 people in this community survive to age 100 using;
  a)

  The Binomial Distribution
  
  
  b)

  The Poisson Distribution
  
  
  c)

  Compare your previous two answers
  
  

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• 4.
  Cumulative Poisson Distribution
  On U.S. route 66 (an American highway) every car that travels this whole route has a probability of $p=0.0002$ of getting into a car accident. A total of 10,000 cars drive this route every month. What is the probability that there are fewer than 3 car accidents in a month?

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• 5.
  Determining the Poisson Distribution using Calculator Commands
  A fair coin is flipped 10 times, what is the probability using the Poisson Distribution commands on your calculator find,
  a)

  The probability that heads comes up 5 times?
  
  
  b)

  The probability that heads comes up 5 or less times?
  
  
  c)

  The probability that heads come up more than 7 times?
  
  

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