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Math Help - Poisson Probability

  1. #1
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    Poisson Probability

    The average number of calls received by a switchboard in a 30-minute period is 15


    a. What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 10 calls?
    b. What is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 15 calls?
    c What is the probability-that between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?

    Not really Sure how to set up.
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  2. #2
    MHF Contributor
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    The Poisson Probability Distribution is very straight-forward. Simply calculate the desired values.

    Pr(n = 10)\;=\;e^{-10}*\frac{10^{10}}{10!}\;=\;0.125

    As long as we are sticking witht he half-hour period already defined, just go with it. No adjustment is required.

    Pr(9\;<\;n\;<\;15)\;=\;e^{-10}*\sum_{n=10}^{14}\left(\frac{10^{n}}{n!}\right)  \;=\;0.459

    You do the last one.
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