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Math Help - Poisson vs. normal approximation

  1. #1
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    Post Poisson vs. normal approximation

    This is just a homework problem from the text that I can't seem to set up right.
    Assume that the background noise X of a digital signal has a normal distribution with \mu = 0 volts and \sigma = 0.5 volt. If we observe n = 100 independent measurements of this noise, what is the probability that at least 7 of them exceed 0.98 in absolute value?


    How would you use the Poisson distribution to approximate this probability?
    Or the normal distribution to approximate this probability?


    Thanks in advance. I was just wondering how one would go about setting this up.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Intsecxtanx View Post
    This is just a homework problem from the text that I can't seem to set up right.
    Assume that the background noise X of a digital signal has a normal distribution with \mu = 0 volts and \sigma = 0.5 volt. If we observe n = 100 independent measurements of this noise, what is the probability that at least 7 of them exceed 0.98 in absolute value?


    How would you use the Poisson distribution to approximate this probability?
    Or the normal distribution to approximate this probability?


    Thanks in advance. I was just wondering how one would go about setting this up.
    The mean number that exceed 0.98 in absolute value is 5 ( 0.98 v is 1.96 \times \sigma).

    So the actual number that exceed 0.98 v: X \sim B(100,0.05).

    This has an approximate normal distribution N(5,100\times 0.05 \times 0.95)

    Also this has an approximate Poisson distribution \text{Pois}(5)

    CB
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