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Math Help - Not sure if this is calc or stat

  1. #1
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    Not sure if this is calc or stat

    I'm trying to figure out the probability that Set A will be higher than set B.

    Set A has an Average of 40 and a standard deviation of 5.
    Set B has an Average of 44 and a standard deviation of 6.

    I thought I would solve for X to figure out how many standard deviations it would take for them to meet, but that doesn't seem to work. To do this I did:
    40 + 5x = 44 + 6x & 40 -5x = 44 -6x
    which results in:
    x = -4 & x = -4



    I suppose I could present a little scenario to illustrate what I am trying to accomplish.

    Suppose Person A's average exam grade = 40 with an SD of 5.
    and that Person B's average exam grade = 44 with an SD of 6.

    What is the probability of person A scoring higher than person B on the next exam.

    I'm not sure if this problem is even possible. Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by QuikLerner View Post
    I'm trying to figure out the probability that Set A will be higher than set B.

    Set A has an Average of 40 and a standard deviation of 5.
    Set B has an Average of 44 and a standard deviation of 6.

    I thought I would solve for X to figure out how many standard deviations it would take for them to meet, but that doesn't seem to work. To do this I did:
    40 + 5x = 44 + 6x & 40 -5x = 44 -6x
    which results in:
    x = -4 & x = -4



    I suppose I could present a little scenario to illustrate what I am trying to accomplish.

    Suppose Person A's average exam grade = 40 with an SD of 5.
    and that Person B's average exam grade = 44 with an SD of 6.

    What is the probability of person A scoring higher than person B on the next exam.

    I'm not sure if this problem is even possible. Any help would be greatly appreciated.
    Are you to assume that the exam grades follow a normal distribution and that the grade of Person A is independent of the grade of Person B?

    It can be done but it might be beyond the scope of what you know. Are you familiar with joint distribution functions and setting up an integral over a region of the xy-plane? Are you familiar with the pdf of a normal distribution?

    It might be best if you post the complete and unexpurgated question exactly as it appears in the book you got it from.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by QuikLerner View Post
    I'm trying to figure out the probability that Set A will be higher than set B.

    Set A has an Average of 40 and a standard deviation of 5.
    Set B has an Average of 44 and a standard deviation of 6.

    I thought I would solve for X to figure out how many standard deviations it would take for them to meet, but that doesn't seem to work. To do this I did:
    40 + 5x = 44 + 6x & 40 -5x = 44 -6x
    which results in:
    x = -4 & x = -4



    I suppose I could present a little scenario to illustrate what I am trying to accomplish.

    Suppose Person A's average exam grade = 40 with an SD of 5.
    and that Person B's average exam grade = 44 with an SD of 6.

    What is the probability of person A scoring higher than person B on the next exam.

    I'm not sure if this problem is even possible. Any help would be greatly appreciated.
    Since no distribution is specified assume normality.

    The difference or two normals is normal with mean equal to the difference of the means, and varianve equal to the sum of the variances.

    CB
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