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Math Help - Distribution and probabilty - parent and sample

  1. #1
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    Exclamation Distribution and probabilty - parent and sample

    Ok I am completely lost, can anyone help me out? I have done the first question, and the second one is based on it.

    The first question said:
    The parent distribution of x is normal with mean 80 and standard deviation 9.
    Based on samples of size n=25, find the mean and standard error of the sampling distribution of \bar{x}.

    I said: \mu_{\bar{x}} = 80
    \sigma_{\bar{x}} = 9/5

    The second question is where I am lost.

    It says find:
    A. P(62 < x < 80)
    B. P(71 < \bar{x} < 77)
    C. x' such that P( \bar{x} > x') = .05
    Last edited by rba_mandy; March 18th 2009 at 09:14 PM. Reason: Wrong symbol >
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  2. #2
    MHF Contributor matheagle's Avatar
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    Is n=25 or 225? Because \sigma_{\bar{x}}={\sigma \over\sqrt{n}}.

    Or, did you mean \sigma_{\bar{x}}={9\over 5}
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  3. #3
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    n=25

    it is the number in the sample
    \sigma\bar{x} = 9/5 (thats what I got) sorry
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  4. #4
    MHF Contributor matheagle's Avatar
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    P(62<X<80)=P\biggl({62-80\over 9}<Z<{80-80\over 9}\biggr)=P(-2<Z<0).

    P(71<\bar X<77)=P\biggl({71-80\over 9/5}<Z<{77-80\over 9/5}\biggr).

    Can you finish these? I'll check on you later.

    .05=P(\bar X<a)=P\biggl(Z<{a-80\over 9/5}\biggr) so {a-80\over 9/5}=-1.645.
    Last edited by matheagle; March 18th 2009 at 09:03 PM.
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  5. #5
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    P[(-5) < z < (-5/3)]

    It was supposed to be P( \bar{x} > x') SORRY

    P( \bar{x} > x'-80\over 9/5) ?

    Can you tell me what formula you used to find that last one?

    Did you use these for the first two?
    Z= X-\mu\over \sigma and Z= \bar{x}-\mu\over \sigma / \sqrt n
    Last edited by rba_mandy; March 18th 2009 at 09:25 PM.
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  6. #6
    MHF Contributor matheagle's Avatar
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    Let X be a random variable with mean \mu and standard deviation \sigma.
    Then Z={X-\mu\over \sigma} has mean zero and standard deviation 1.
    And if X was a normal random variable, then Z is a standard normal random variable and you can use your Z table.
    We did that for both X and \bar X.
    Last edited by matheagle; March 19th 2009 at 03:59 PM.
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  7. #7
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    Smile

    Thank you SO much for your help. It helped me a lot on my test. Thanks a hundred times. You are a really nice person
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