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    Normal probability calculation

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    #1
    The average number of customer complaints at the Full Moon Motel is five per day.
    Find the probability that on a typical day, the motel will receive

    a) eight complaints
    b) at least two complaints

    #2
    Demand for a product is normal, with mean being 400 and standard deviation being 25 units. Find

    a) Pr (demand > 445)
    b) Pr (demand is between 375 and 425)
    c) Pr (demand equals 400)
    d) Pr (demand exceeds 500)
    e) The 5 percentile demand level

    #3The sales of a product are uniformly distributed between 300 and 800. Find

    a) Probability (Sales < 500)
    b) Probability (Sales between 700 and 900)
    c) Probability of sales exactly equal to 750
    d) 15 percentile sales level

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    https://brainmass.com/statistics/probability-density-function/normal-probability-calculation-142214

    Solution Preview

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    Statistics Business

    #1 The average number of customer complaints at the Full Moon Motel is five per day.
    Find the probability that on a typical day, the motel will receive

    a) Eight complaints
    b) At least two complaints
    Answer
    Let X be the number of complaints at the Full Moon Motel. Given that X is Poisson with mean  = 5. The probability density function of Poisson random variable is given by
    The probabilities for different values of X are given below

    X P(X=x)
    0 0.006737947
    1 0.033689735
    2 0.084224337
    3 0.140373896
    4 0.17546737
    5 0.17546737
    6 0.146222808
    7 0.104444863
    8 0.065278039
    9 0.036265577

    a). P(X=8) = 0.065278039
    b). ...

    Solution Summary

    This solution gives the step by step method for computing probability from normal distribution.

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