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Math Help - the normal distribution question help

  1. #1
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    the normal distribution question help

    Hi,

    I am new here, and I hope you can help.

    Here is the question:

    One year, the distribution of salaries for professional sports players had mean $1.5 million and standard deviation $0.9 million. Suppose a sample of 400 major leagu0e players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million.

    The correct answer is approximately 1, but I can't figure out how to work it out.

    So far I have tried resolving it by following
    z= 1,100,000-1,500,000/900,000 = 0.4 which according to the z table translates to .1554

    Then I subtracted this number from .5 which resulted in .3446 which I take it to mean that approximately 34% of players earn more than 1.1million.

    How do I use the 400 baseball players in this equation?

    Thanks
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  2. #2
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    Re: the normal distribution question help

    The standard deviation of sample means = 0.9/sqrt400
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  3. #3
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    Re: the normal distribution question help

    0.9 / sqrt(400) = 0.045

    but...I still don't know how to solve the original question. How do I get to the answer that approximately 1 player's salary exceeds 1.1 million? Please be as explicit as possible.

    thanks.
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  4. #4
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    Re: the normal distribution question help

    The question asks for the P that the average salary of 400 players exceeds 1.1

    So we want P(Z> (1.1-1.5)/0.045) That is P(Z>-8.89) which from tables is approx. 1
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  5. #5
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    Re: the normal distribution question help

    thank you so much
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