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Math Help - Approximate probability of sample mean

  1. #1
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    Approximate probability of sample mean

    A participant in a walk-a-thon has sponsor donations (in dollars) with a mean of 2000 and a standard deviation of 500. A random sample of size n=25 is taken from all of this participant's sponsor donations and the sample mean x is considered. Approximate P(X>2050). (Both x's should have a line above them to denote sample mean)

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  2. #2
    MHF Contributor matheagle's Avatar
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     P(\bar X>2050) = P\biggl( {\bar X-2000\over 500/\sqrt{25}}> {2050-2000\over 500/\sqrt{25}}\biggr)

    then by the CLT  \approx P\biggl( Z> {2050-2000\over 500/\sqrt{25}}\biggr)=P( Z> .5).
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  3. #3
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    Is this to be calulated by subtracting the normal distribution (0.9332) from 1? If so, I believe my answer should be 0.0668. Am I correct?
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  4. #4
    MHF Contributor matheagle's Avatar
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    I don't think .9332 is correct. Look at the st normal tables again.
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  5. #5
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    I'm sorry, i was looking at the wrong problem. I think the answer is just 0.3085.
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  6. #6
    MHF Contributor matheagle's Avatar
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    that seems more reasonable
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  7. #7
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    It is really that simple? The table basically gives you the answer, as long as you set up the equation correctly?
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