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Math Help - Urgent Stats problem

  1. #1
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    Urgent Stats problem

    I'm struggling with a stats problem....can anyone help me out. I don't just want an answer I want to know how to do the work.

    Thanks

    Jimís score on a Stats Exam was 0.4 SD above the mean. What are the 2 possible z-scores Joe would need to obtain for the area under the curve between Jim and Joe to be 27%? Assume the Stats Exam is normally distributed. Show work.

    Any help appreciated. Thanks!
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  2. #2
    Senior Member tukeywilliams's Avatar
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    You know that 68% of the scores lies in the interval  [\mu - \sigma, \mu + \sigma] . So you know that Jim's score is  \mu + 0.4 \sigma .
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  3. #3
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    Quote Originally Posted by tukeywilliams View Post
    You know that 68% of the scores lies in the interval  [\mu - \sigma, \mu + \sigma] . So you know that Jim's score is  \mu + 0.4 \sigma .
    Thanks for the quick response. But I am still confused. I have not been given any of the values, and the question is as phrased. So I have no idea where to go from here to find Joe's two scores. I know the definitions but I am bad at figuring out what the question wants me to do. Can you give me some more directions like how do I use the 27%, and how do I determine Joe's score.
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  4. #4
    Senior Member tukeywilliams's Avatar
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    Assume the standard normal distribution (i.e.  \mu = 0, \sigma = 1 ). Then Jims score is  0.4 or  z = 0.4 . So I used a table and got one of the z-scores as  z = -0.3 . The other one was  z  = 1.5 . The area is approx.  0.27 .

    So  \frac{\mu + 0.4 \sigma - \mu}{\sigma} = 0.4 = z (we standardize the z-score). They ask for 2 possible z-scores because you can have a z-score greater than or less than  0.4 such that the area is  0.27 . We are using one of those z-score tables in the back of a stats book.
    Last edited by tukeywilliams; July 22nd 2007 at 11:15 AM.
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  5. #5
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    How did you use the 27% to get those numbers? What kind of a table are we using? I need to show my work for full credit. Thanks again for your help!

    Just saw your edit, let me see if it makes sense. Thanks!!
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  6. #6
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    Quote Originally Posted by tukeywilliams View Post
    Assume the standard normal distribution (i.e.  \mu = 0, \sigma = 1 ). Then Jims score is  0.4 or  z = 0.4 . So I used a table and got one of the z-scores as  z = -0.3 . The other one was  z  = 1.5 . The area is approx.  0.27 .

    So  \frac{\mu + 0.4 \sigma - \mu}{\sigma} = 0.4 = z (we standardize the z-score). They ask for 2 possible z-scores because you can have a z-score greater than or less than  0.4 such that the area is  0.27 . We are using one of those z-score tables in the back of a stats book.
    OK, the logic makes perfect sense, but I'm not sure how to read the z score table to see how you got the two numbers... OMG i don't think my stats teacher is teaching us what we need to know!!

    Help!
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  7. #7
    Senior Member tukeywilliams's Avatar
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    you can also use some of those online calculators that calculates z-scores. That is probably more accurate than tables. Google 'z-score calculators.'

    Or Distribution Tables

    The left hand numbers (bold ones) are the z scores, and the right hand numbers are the area to the left of the particular point. So I found the area and matched it with the z-score.

    Notice that  0.43 - 0.15 = 0.28 which is the the difference between the z-scores  1.5 and  0.4 in the table. So its not exact, but close enough.
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  8. #8
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    Quote Originally Posted by tukeywilliams View Post
    you can also use some of those online calculators that calculates z-scores. That is probably more accurate than tables. Google 'z-score calculators.'

    Or Distribution Tables

    The left hand numbers (bold ones) are the z scores, and the right hand numbers are the area to the left of the particular point. So I found the area and matched it with the z-score.

    Notice that  0.43 - 0.15 = 0.28 which is the the difference between the z-scores  1.5 and  0.4 in the table. So its not exact, but close enough.

    What do the bold numbers at the top of the table correspond to? Thanks again, it's definitely starting to make more sense!. I am going to try and solve a few more problems and see if I have followed it all.
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  9. #9
    Senior Member tukeywilliams's Avatar
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    Look at the z-score  1.0 . Go to the third entry. It says  0.3461 . The bold number above is  0.02 . So the area corresponds to z-score  1.02 .
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  10. #10
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    Quote Originally Posted by tukeywilliams View Post
    Look at the z-score  1.0 . Go to the third entry. It says  0.3461 . The bold number above is  0.02 . So the area corresponds to z-score  1.02 .
    ahhh.. that makes sense. Thanks again!
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