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Math Help - Tree Rings

  1. #1
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    Tree Rings

    The following data represents the ages of trees drawn as a random sample of trees in a park in Canada. The data was collected by park officials, and the numbers represent the number of rings in the trunk of the tree. Each ring represents one year of growth for a tree.

    26 30 48 22 47 42 25 25 29 5 18
    4 23 16 36 26 36 35 36 2 39 15
    37 29 37 16 15 48 9 12 41 41 32
    26 14 5 6 46 21 15 1 26 43 27

    1. Use IT to determine the mean, median, range, and standard deviation for the data.

    2. Use the results of #1 to determine if the sample is normally distributed. Explain your reasoning.

    3. What would be the z-score of a tree with 33 rings? Explain how you arrived at your answer.

    4. If you assume that the data are normally distributed, what percentage of the trees would have from 17 to 38 inclusive rings? Explain how you arrived at your answer.

    5. Find the 95 percent confidence interval and the margin of error for the ages of the trees in the sample. Explain how you arrived at your answer.



    So, I put the numbers in order first of all to make it easier;
    1,2,4,5,5,6,9,12,14,15,15,15,16,16,18,21,22,23,25, 25,26,26,26,26,
    27,29,29,30,32,35,36,36,36,37,37,39,41,41,42,43,46 ,47,48,48

    1. The mean (average) is 25.73
    The median is 26
    The range is 1-48

    then I'm not really sure what standard deviation is, and I'm completely lost after that simple stuff...
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  2. #2
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    Quote Originally Posted by goldensports86 View Post
    The following data represents the ages of trees drawn as a random sample of trees in a park in Canada. The data was collected by park officials, and the numbers represent the number of rings in the trunk of the tree. Each ring represents one year of growth for a tree.

    26 30 48 22 47 42 25 25 29 5 18
    4 23 16 36 26 36 35 36 2 39 15
    37 29 37 16 15 48 9 12 41 41 32
    26 14 5 6 46 21 15 1 26 43 27

    1. Use IT to determine the mean, median, range, and standard deviation for the data.

    2. Use the results of #1 to determine if the sample is normally distributed. Explain your reasoning.

    3. What would be the z-score of a tree with 33 rings? Explain how you arrived at your answer.

    4. If you assume that the data are normally distributed, what percentage of the trees would have from 17 to 38 inclusive rings? Explain how you arrived at your answer.

    5. Find the 95 percent confidence interval and the margin of error for the ages of the trees in the sample. Explain how you arrived at your answer.



    So, I put the numbers in order first of all to make it easier;
    1,2,4,5,5,6,9,12,14,15,15,15,16,16,18,21,22,23,25, 25,26,26,26,26,
    27,29,29,30,32,35,36,36,36,37,37,39,41,41,42,43,46 ,47,48,48

    1. The mean (average) is 25.73
    The median is 26
    The range is 1-48

    then I'm not really sure what standard deviation is, and I'm completely lost after that simple stuff...
    Actually, the range is \textrm{max} - \textrm{min} = 48 - 1 = 47.

    What technology are you using?
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