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Poisson Distribution quiz

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  • What is the Poisson distribution used to model?
    It models the number of occurrences over a fixed interval, such as time or space, given a mean rate of occurrence.
  • What is the key parameter of the Poisson distribution and what does it represent?
    The key parameter is lambda (λ), which represents the mean rate of occurrence over the interval.
  • How do you calculate the probability of exactly x occurrences in a Poisson distribution?
    Use the formula: λ^x * e^(-λ) / x! where x is the number of occurrences.
  • What are the conditions for a Poisson experiment?
    You need a fixed interval, independent intervals, and a constant mean rate of occurrence.
  • How can you recognize a Poisson experiment in a word problem?
    Look for a fixed interval and mention of an average or mean rate, such as 'per hour' or 'every minute.'
  • What is the mean of a Poisson distribution?
    The mean is equal to lambda (λ).
  • What is the variance of a Poisson distribution?
    The variance is also equal to lambda (λ).
  • How do you find the standard deviation of a Poisson distribution?
    Take the square root of lambda (λ).
  • When can you use the Poisson distribution to estimate binomial probabilities?
    When the number of trials is large (at least 100) and the probability of success is small (n*p ≤ 10).
  • How do you determine lambda (λ) when estimating binomial probabilities with the Poisson formula?
    Set λ equal to n*p, where n is the number of trials and p is the probability of success.
  • What calculator function is used to find the probability of exactly x occurrences in a Poisson distribution?
    Use Poisson PDF on a TI-84 calculator.
  • What calculator function is used to find the probability of at most x occurrences in a Poisson distribution?
    Use Poisson CDF on a TI-84 calculator.
  • What does Poisson CDF calculate?
    It calculates the probability that the number of occurrences is less than or equal to a specified value.
  • How is the Poisson distribution different from the binomial distribution in terms of what is fixed?
    Poisson has a fixed interval (often time), while binomial has a fixed number of trials.
  • What is a typical indicator in a problem that suggests using the Poisson distribution?
    Mention of an average rate or mean rate per interval, such as '3.6 birds per hour.'