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Poisson distribution for insurance

  1. Sep 29, 2011 #1
    1. The problem statement, all variables and given/known data

    An insurer uses the Poisson distribution with mean 4 as the model for the number
    of warranty claims per month on a particular product. Each warranty claim results
    in a payment of 2 by the insurer. Find the probability that the total payment by
    the insurer in a given month is less than two standard deviations above the average
    monthly payment.

    2. Relevant equations

    3. The attempt at a solution
    So, mean = 4
    Standard deviation = 2

    Will I use the density function to solve this?
  2. jcsd
  3. Sep 29, 2011 #2


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    Mean of what is 2? Standard deviation of what is 2? Where did the 2 come from?

    You need to define your variables to get started. If X is the number of warranty claims in a month then the mean of X is 4. What is the std deviation of X? If Y is the amount paid in claims in a month, then isn't Y = 2X? Y and X aren't the same thing. Can you get the mean and std deviation of Y? Can you get going from this?
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