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Math Help - expected values

  1. #1
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    Arrow expected values

    A book store orders only 3 copies of a certain math book per month, because the manger does not believe that more will be sold. If the number of requests follows a Poisson distribution with mean 36 per year,

    1. what is the expected number of copies sold every months?

    2. how many copies should the store manager order such that the probability of running out of copies is less than 5%?
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  2. #2
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    Quote Originally Posted by Statsnoob2718 View Post
    A book store orders only 3 copies of a certain math book per month, because the manger does not believe that more will be sold. If the number of requests follows a Poisson distribution with mean 36 per year,

    1. what is the expected number of copies sold every months?

    2. how many copies should the store manager order such that the probability of running out of copies is less than 5%?
    1. Let X be the random variable number of books sold per month. Then \lambda = E(X) = \frac{36}{12} = 3.

    2. You require the value of x such that \Pr(X > x) < 0.05 \Rightarrow \Pr(X \leq x) > 0.95. So find the smallest value of x such that \sum_{i = 0}^x\frac{e^{-3} 3^i}{i!} > 0.95. I suggest using technology.
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