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Math Help - sampling distribution

  1. #1
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    sampling distribution

    Hi,

    I need help about 2 problems. It is about sampling distribution.

    PROBLEM 1:
    Assume the octane rating for a particular type of gasoline is normally distributed ramdom variable with a mean=87.0 and standard deviation=1.5.
    -What is the probability the mean of a random sample mean of 5 measurements of the octane rating for this type of gasoline will be between 86.5 and 87.5?


    Here I wanted to use the central limit theorem but the sample is not large enough. So I don't kow how to do it.

    PROBLEM 2
    Suppose the probability that a communication is a signal, X=1, is 0.9, and the probability that a communication is noise, X=0, is 0.1. A random sample of 3 communications is to be taken, the value X, 0, 1, recorded and mean(X) computed. Find the sampling distribution of mean(X).
    ??


    Thank you
    B
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by braddy View Post
    Hi,

    I need help about 2 problems. It is about sampling distribution.

    PROBLEM 1:
    Assume the octane rating for a particular type of gasoline is normally distributed ramdom variable with a mean=87.0 and standard deviation=1.5.
    -What is the probability the mean of a random sample mean of 5 measurements of the octane rating for this type of gasoline will be between 86.5 and 87.5?

    Here I wanted to use the central limit theorem but the sample is not large enough. So I don't kow how to do it.
    You don't need the central limit theorem, what you need is the fact that
    the mean of a sample of size N from a normal distribution N(mu, sigma^2)
    is itself normal distributed ~N(mu, sigma^2/N).

    So in this case the mean of the sample means is m5 = 87.0, and the standard deviation of the sample means is s5 =1.5/sqrt(5).

    Now the interval 86.5 to 87.5 is the interval m5 - 0.75 s5 to m5 - 0.75 s5
    or a +/-0.75 sd interval about the mean. The probability of this we look up
    in a table of the standard normal distribution and is ~=0.4532

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by braddy View Post
    PROBLEM 2
    Suppose the probability that a communication is a signal, X=1, is 0.9, and the probability that a communication is noise, X=0, is 0.1. A random sample of 3 communications is to be taken, the value X, 0, 1, recorded and mean(X) computed. Find the sampling distribution of mean(X).
    ??
    I don't understand what you are asking here

    RonL
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