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Math Help - Normal distribution Question

  1. #1
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    Normal distribution Question

    A factory manufactures steel poles; the length of the poles are approximately normally dis-
    tributed with mean 75cm with standard deviation 1cm. Find the probability that a randomly
    selected pole will be between 74.5 and 75.8cm.


    Ok What i get when i try to transform this to the standard normal is

    Z = .8 for X 75.8

    and -.5 for X 74.5

    I dont know what to do from here.

    Any help greatly appreciated.

    Thanks
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  2. #2
    Senior Member TriKri's Avatar
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    You should look up in a table how big the chance is that a N(0, 1) distributed number is < 0.8, then take 1 - that to get the risk of falling outside. Then you should do the same thing the check the chanse that a N(0, 1) number is > -0.5. You then add the chances of falling outside. You now get the total risk of falling outside, on any of the sides. Take 1 - that to get the probability that a pole is between 74.5 and 75.8.

    Note: Your table may not cover negative numbers (this is most likely). Then realize that the chance of the number being > -0.5 is the same as the chance of the number being < 0.5, because of the symmetry around 0.
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  3. #3
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    Hey thanks, I tried to look up in a tables but for 0.8 there were 5 different values in the row.
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  4. #4
    Senior Member TriKri's Avatar
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    There should be only one value. Are you looking in the right table? Ask someone about how to use it if you are not sure how to use the table.
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  5. #5
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    Hi thanks for your reply I have this table Standard Normal Distribution Table I think the previous one i was looking at was incorrect.

    so for .8 the area is .2881

    and for .5 the area is .1915

    so 1 - .2881 = .7119

    and to fall outside of -.5 its .1915

    Then the answer is 1 - ( .1915 + .7119) = .0966??

    This seams too small
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  6. #6
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    p(-0.5<Z<0.8) = .2881 + .1915 (using your figures) = 0.4796
    I always find it best to draw a quick diagam so see if you need to add or subtract areas.

    The table you referred to gives area from z=0 out. Some tables give the area from the left tail. Just be aware of what your table is giving you.
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  7. #7
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    Hey thanks so much!! We have never even discussed these tables in class and I had spent ages trying to to the integration without joy until i found out about these online.
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