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Math Help - Hi, new here! Was wondering if I am right, I would

  1. #1
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    Arrow Hi, new here! Was wondering if I am right, I would

    I would rather try things out as far as they can go, and then ask for help!

    I am having problems on a statistics problem, that goes like this:

    Suppose that a random variable X observes normal distribution N~(58.2, 12.55).

    1)Calculate P(X>25)

    For this I find the z-score. Z=X-M/S, X=random variable, M=mean, S=standard deviation. So, Z=X-M/S = 25-58.2/12.55= -2.65. This is where I am confused. After this I have P(X>25)= 0.50-P(-2.65<X<0)= 0.004. I am not sure if I am right on this.

    The second part of the question, still keeping the same mean and standard deviation, goes like this:

    Calculate P(49.6<X<65.3) I converted each X into a z-score:

    Z=65.3-58.2/ 12.55= 0.56
    Z=49.6-58.2/ 12.55= -0.69

    Then I looked up each z-score in a normal table in my statistics book to find the percentage that corresponds to each z-score: (Did I do my notation right, by the way?)

    For z-score 0.56: P(0<X<0.56)= 0.2123
    For z-score -0.69: P(0<X-0.29)= 0.1141

    Finding z-scores then looking in a normal table to find percentages/probability is easy, but I get lost here. I don't know how to "complete" the problem and answer what is being asked of me. Help please? What am I lost on?
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  2. #2
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    Quote Originally Posted by peanutbutter View Post
    I would rather try things out as far as they can go, and then ask for help!

    I am having problems on a statistics problem, that goes like this:

    Suppose that a random variable X observes normal distribution N~(58.2, 12.55).

    1)Calculate P(X>25)

    For this I find the z-score. Z=X-M/S, X=random variable, M=mean, S=standard deviation. So, Z=X-M/S = 25-58.2/12.55= -2.65. This is where I am confused. After this I have P(X>25)= 0.50-P(-2.65<X<0)= 0.004. I am not sure if I am right on this.

    [snip]
    1) Your answer is wrong. Since 25 is much less than the mean value of 58.2, you would certainly expect Pr(X > 25) to be greater than 0.5 and in fact you should expect the answer to be quite close to 1 since 25 is more than two standard deviations away from the mean .....

    Pr(X > 25) = Pr(Z > -2.65) = Pr(Z < 2.65) by symmetry.

    So your answer should be 1 - 0.004 = 0.996 (assuming you're using tables).

    I'll get to the second part later.
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  3. #3
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    Quote Originally Posted by peanutbutter View Post
    The second part of the question, still keeping the same mean and standard deviation, goes like this:

    Calculate P(49.6<X<65.3) I converted each X into a z-score:

    Z=65.3-58.2/ 12.55= 0.56
    Z=49.6-58.2/ 12.55= -0.69

    Then I looked up each z-score in a normal table in my statistics book to find the percentage that corresponds to each z-score: (Did I do my notation right, by the way?)

    For z-score 0.56: P(0<X<0.56)= 0.2123
    For z-score -0.69: P(0<X-0.29)= 0.1141 Mr F says:

    Finding z-scores then looking in a normal table to find percentages/probability is easy, but I get lost here. I don't know how to "complete" the problem and answer what is being asked of me. Help please? What am I lost on?
    Note that Pr(49.6 < X < 65.3) = Pr(-0.69 < Z < 0.56) = Pr(-0.69 < Z < 0) + Pr(0 < Z < 0.56) = Pr(0 < Z < 0.69) + Pr(0 < Z < 0.56) = ........
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