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Poisson Distribution quiz

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  • What is the main difference between the binomial and Poisson distributions in terms of what is fixed?
    The binomial distribution has a fixed number of trials, while the Poisson distribution has a fixed interval, usually time.
  • What is the key parameter (mean rate) called in the Poisson distribution?
    The key parameter is called lambda (λ), which represents the mean rate of occurrence over the interval.
  • What formula is used to calculate Poisson probabilities?
    The formula is P(X = x) = λ^x * e^(-λ) / x!.
  • What are the three main conditions for a Poisson experiment?
    The conditions are: a fixed interval, independent intervals, and a constant mean rate of occurrence.
  • How do you recognize a Poisson experiment in a word problem?
    Look for a fixed interval and mention of an average or mean rate, often described as 'something per something.'
  • In the Poisson distribution, what is the mean equal to?
    The mean is equal to lambda (λ).
  • How do you find the standard deviation in a Poisson distribution?
    The standard deviation is the square root of lambda (√λ).
  • When can you use the Poisson distribution to approximate a binomial probability?
    When the number of trials (n) is at least 100 and n*p is less than or equal to 10.
  • How do you determine lambda (λ) when using the Poisson distribution to approximate a binomial distribution?
    Set lambda equal to n*p, where n is the number of trials and p is the probability of success.
  • What calculator function do you use to find the probability of exactly x occurrences in a Poisson distribution?
    Use the Poisson PDF function on your calculator.
  • What calculator function do you use to find the probability of at most x occurrences in a Poisson distribution?
    Use the Poisson CDF function on your calculator.
  • If the average rate of cars passing an intersection is 17.6 per minute, what is lambda for the Poisson distribution?
    Lambda (λ) is 17.6.
  • What does the Poisson CDF function calculate?
    It calculates the cumulative probability that the number of occurrences is less than or equal to a specified value.
  • Why is the Poisson probability formula considered easier than the binomial probability formula?
    It has fewer terms and only requires the mean rate (λ), making calculations simpler, especially for large n and small p.
  • What is the variance of a Poisson distribution?
    The variance is equal to lambda (λ).