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Math Help - probability...normal distribution

  1. #1
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    probability...normal distribution

    Assume you have a Normal Distribution with a mean of 7.5 and a standard deviation of 3.

    • What is the probability that X is greater than 8.5?


    • What is the probability that X is greater than 6.5?.


    • What is the probability that X is greater than 3 but less than 5.5?


    • What is the probability that X is less than 7.5?
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  2. #2
    Bar0n janvdl's Avatar
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    Excuse me if this is wrong, I only started with it today in class... But seeing as no-one else is answering I might as well take the chance and see if I can help.

    Quote Originally Posted by sdudley24 View Post
    Assume you have a Normal Distribution with a mean of 7.5 and a standard deviation of 3.


    • What is the probability that X is greater than 8.5?



    P(X > 8,5)

    = 1 - P(X < 8,5)

    = 1 - P( \frac{X - 7,5}{3} < \frac{8,5 - 7,5}{3} )

    = 1 - P(Z < \frac{1}{3})

    = 1 - \Phi (\frac{1}{3})

    = 1 - 0,6293

    = 0,3707


    • What is the probability that X is greater than 6.5?.


    P(X > 6,5)

    = 1 - P(X < 6,5)

    = 1 - P( \frac{X - 7,5}{3} < \frac{6,5 - 7,5}{3} )

    = 1 - P(Z < - \frac{1}{3})

    = 1 - \Phi (- \frac{1}{3})

    = 1 - 0,3707

    = 0,6293

    • What is the probability that X is greater than 3 but less than 5.5?


    P(3 < X < 5,5)

    = P( \frac{3 - 7,5}{3} < \frac{X - 7,5}{3} < \frac{5,5 - 7,5}{3} )

    = P(- \frac{3}{2} < Z < - \frac{2}{3})

    = \Phi (- \frac{2}{3}) - \Phi (- \frac{3}{2})

    = 0,2514 - 0,0668

    = 0,1846

    • What is the probability that X is less than 7.5?


    P(X < 7,5)

    = P( \frac{X - 7,5}{3} < \frac{7,5 - 7,5}{3} )

    = P(Z < 0)

    = \Phi (0)

    = 0,5000
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  3. #3
    Member Danshader's Avatar
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    correct jan xD
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