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    Probability Distribution

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    1)
    The time it takes for a light bulb to burn out.
    Continuous

    The weight of a t-bone steak
    Continuous

    The number of people in class who have type B blood.
    Discrete

    2) The mean (expected value) of the random variable is

    3) The variance of the random variable is

    4) The standard deviation of the random variable is

    5) The probability that Apu sells exactly 8 tofu dogs in a day is

    6) The probability that Apu sells 7 or more tofu dogs in a day is

    7) Let X denote the payoff. Then X can take the following values

    8) A simple random sample of 40 students are asked whether they have internet access at home. The number of students who do have home access is recorded

    9) If X follows a binomial distribution with parameters n and p, the probability distribution of X is given by,

    10) ) If X follows a binomial distribution with parameters n and p, the probability distribution of X is given by,

    11) The mean of the random variable is

    12) The standard deviation of the random variable is

    13) The probability that x<4 is given by,

    14) Let X denote the number of patients who experienced weight gain as a side effect in a random sample of 50.

    15) The probability that 8 or fewer experienced weight gain as a side effect is given

    16) The probability that 6 or more patients experienced weight gain as a side effect is

    17) According to the range rule of thumb, most values should lie within 2 standard deviations from the mean. We can therefore identify "unusual" values by determining if they lie outside these limits:

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    Please see the Excel file for computation.

    1)
    The time it takes for a light bulb to burn out.
    Continuous

    The weight of a t-bone steak
    Continuous

    The number of people in class who have type B blood.
    Discrete

    2) The mean (expected value) of the random variable is

    = 5.741
    3) The variance of the random variable is

    = 39.073 - (5.741)2
    = 6.1139
    = 6.114
    4) The standard deviation of the random variable is

    = 2.4726
    = 2.473
    5) The probability that Apu sells exactly 8 tofu dogs in a day is
    P(x = 8) = P(8) = 0.076
    6) The probability that Apu sells 7 or more tofu dogs in a day is

    = P(7) + P(8) + P(9) + P(10) + P(11)
    = 0.094 + 0.076 + 0.058 + 0.054 + 0.055
    = 0.337
    7) Let X denote the payoff. Then X can take the following values
    X = $680 if the property in question will not be destroyed by a flood
    = $680 - $800,000 = -$799,320, if the property will be destroyed by a flood
    Here it is given that the probability that the property in question will be destroyed by a flood in the coming year is 0.0003265.
    Thus the ...

    Solution Summary

    The solution discusses the application of various tools in statistics using probability theory.

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