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Math Help - normal distribution with a mean and standard deviation...I am lost

  1. #1
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    normal distribution with a mean and standard deviation...I am lost

    X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
    (A) P(x < 77.0)
    (B) P(75.0 < x < 85.0)
    (C) P(x > 85.0)
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  2. #2
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    A)

    Find the z value fot x = 77.

    z = \dfrac{x - \mu}{\sigma} = \dfrac{77 - 80}{3.5} = -0.857

    So, you have
    P(X < 77) = P(z < -0.857)

    Look up your z table for the corresponding probability.

    Do the same for the others.

    B) P(75.0 <X< 85.0) = P(\dfrac{75 - 80}{3.5} < z < \dfrac{85 - 80}{3.5}) = P( -1.429 < z < 1.429)

    C) P(X > 85.0) = P(z > 1.429)

    Post what you get!
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  3. #3
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    Quote Originally Posted by caligirl350 View Post
    X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
    (A) P(x < 77.0)
    (B) P(75.0 < x < 85.0)
    (C) P(x > 85.0)
    Sorry, but these are very routine questions - I suggest you go to your class notes or textbook and review the examples that are certain to be there.
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