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Math Help - Normal distribution and confidence intervals

  1. #1
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    Normal distribution and confidence intervals

    Hello,

    I am looking for a little guidance or help with the following question:

    The standard deviation of the masses of 600 blocks is 248 kg.
    A random sample of 55 blocks has a mean mass of 4.72 Mg.
    With what degree of confidence can it be said that the mean mass of all the blocks is 4.72 0.100 Mg?

    I've tried reading up some information on the normal distribution table but can't really get my head around it. Could anyone offer me some advice or provide me with a good link with information on the subject?

    Thanks.
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  2. #2
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    Re: Normal distribution and confidence intervals

    I am not an expert on this stuff, but I think you need to figure out the standard error for your sample. Once you know standard error, you can use it to judge how close your estimate for the mean should be and with what confidence level. Essentially, standard error is the standard deviation of your sample. So, if you were to find the mean mass of every possible sample (from 1 block, all the way up to 600 blocks), you should be able to calculate the approximate standard deviation of the set of samples based on the actual standard deviation of the masses and the size of your sample. So, using the binomial theorem, since your sample is greater than 30 blocks, you can use the formula that standard error is standard deviation over the square root of your sample size.

    \text{St Err}=\frac{\sigma}{\sqrt{n}}

    Where \sigma is your standard deviation of 0.248Mg=248kg, and your sample size n=55. Need any more assistance?
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Normal distribution and confidence intervals

    Quote Originally Posted by StephenB1965 View Post
    The standard deviation of the masses of 600 blocks is 248 kg.
    A random sample of 55 blocks has a mean mass of 4.72 Mg.
    With what degree of confidence can it be said that the mean mass of all the blocks is 4.72 0.100 Mg?...
    Assuming a normally distributed population without replacement samples:

    Population size = N =600
    Sample size =n = 55
    \sigma =248

    then, sample standard error:

    s=\frac{\sigma }{\sqrt{n}}*\sqrt{\frac{\text{N}-n}{\text{N}-1}} = 31.897

    and z value is:

    z=\pm \frac{100}{s}=\pm 3.1351

    Now find probability from a normal distribution table.
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  4. #4
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    Re: Normal distribution and confidence intervals

    Many thanks but I thought the sample standard error was calculated by:
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    Re: Normal distribution and confidence intervals

    StephenB1965,

    I am also looking for how to figure out confidence intervals when I only have a mean of a sample and a SD of the population. If you get any luck, drop me a message will keep checking this post though.

    Also, I thought the standard error of the mean was

    SE = Standard Error of Population Mean
    SD = Standard Deviation of Population

    SE = SD/sqrrt(SampleSize)
    Last edited by JungleMath; September 27th 2012 at 02:39 PM.
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    Re: Normal distribution and confidence intervals

    Quote Originally Posted by MaxJasper View Post
    and z value is:

    z=\pm \frac{100}{s}=\pm 3.1351

    Now find probability from a normal distribution table.

    MaxJasper, what is the z value for?
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  7. #7
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Normal distribution and confidence intervals

    Quote Originally Posted by JungleMath View Post
    MaxJasper, what is the z value for?
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    Re: Normal distribution and confidence intervals

    Thank you very much, helped out alot.
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  9. #9
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    Re: Normal distribution and confidence intervals

    Thanks for your help so far MaxJasper, one quick query tho, to get the s value (which I presume is the sample standard error) why do you have to multiply the standand error by √N n / N - 1?
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  10. #10
    Senior Member MaxJasper's Avatar
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    Re: Normal distribution and confidence intervals

    Normal distribution assumes N=infinite, when N<inf then the modified version is used for sample standard error.
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