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Math Help - theoretical distribution

  1. #1
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    theoretical distribution

    Let X denote the length in millimeters of an organism. Assume that this variable X is Normally distributed with mean 12.2 and standard deviation 5.6. Let X denote the sample mean length for any random sample of four organisms.
    What is the (theoretical) distribution of all such X's?

    They give us a page of different sized organisms...im thinking this means i have to measure all of them or 4 of them
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  2. #2
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    Quote Originally Posted by rmweeks View Post
    Let X denote the length in millimeters of an organism. Assume that this variable X is Normally distributed with mean 12.2 and standard deviation 5.6. Let X denote the sample mean length for any random sample of four organisms.
    What is the (theoretical) distribution of all such X's?

    They give us a page of different sized organisms...im thinking this means i have to measure all of them or 4 of them
    The distribution of sample means of samples of size N drawn from a normal distribution N(mu, sigma^2) is:

    N(mu,sigma^2 / N),

    so in this case X is normally distributed with mean 12.2 and SD 5.6/2 = 2.8.

    RonL
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