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    7.
    During term time, incoming calls to a school are thought to occur at a rate of 0.45 per
    minute. To test this, the number of calls during a random 20 minute interval, is recorded.
    (b) Find the critical region for a two-tailed test of the hypothesis that the number of
    incoming calls occurs at a rate of 0.45 per 1 minute interval. The probability in each
    tail should be as close to 2.5% as possible.
    Can someone explain to me why you use the poisson distribution instead of binomial in this situation.
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    Because you have a seemingly random variable, a mean rate and a time interval.

    Or something like that.
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    because apparently the poisson fits it better.

    like if you took a huge sample and plot them it would look more like a poisson and binomial.

    but there may be a theoretical/intuitive reason, but i dont know.
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    (Original post by MIKE ESSIEN IS QUITE SICK)
    7.
    During term time, incoming calls to a school are thought to occur at a rate of 0.45 per
    minute.
    To test this, the number of calls during a random 20 minute interval, is recorded.
    (b) Find the critical region for a two-tailed test of the hypothesis that the number of
    incoming calls occurs at a rate of 0.45 per 1 minute interval. The probability in each
    tail should be as close to 2.5% as possible.
    Can someone explain to me why you use the poisson distribution instead of binomial in this situation.
    Normally this is the biggest clue you can get.
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    (Original post by MIKE ESSIEN IS QUITE SICK)
    7.
    During term time, incoming calls to a school are thought to occur at a rate of 0.45 per
    minute. To test this, the number of calls during a random 20 minute interval, is recorded.
    (b) Find the critical region for a two-tailed test of the hypothesis that the number of
    incoming calls occurs at a rate of 0.45 per 1 minute interval. The probability in each
    tail should be as close to 2.5% as possible.
    Can someone explain to me why you use the poisson distribution instead of binomial in this situation.
    The Poisson distribution is used when you are looking at the number of times an event happens in a certain length of time (or space).

    If you have doubts when picking between the 2 distributions, there are 2 things you can look for:
    1) Does the word "per" appear in the question? If so, it's probably Poisson. In this case the answer was yes, "per 1 minute interval".
    2) Can you put a number to the maximum number of events that could occur? If yes, it's Binomial, if no (as in this case) it's Poisson.

    Neither of these personal aids should be used to answer "why is the Poisson distribution appropriate in this situation?" For this question, stick to "calls occur at a constant rate, independently, singly"
 
 
 
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