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Math Help - Confidence Levels

  1. #1
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    Confidence Levels

    A set of metal bars are known to have a mean diameter of 13.03mm with standard deviation of 0.63mm. If it can be assumed that diameters are normally distributed:
    i. find the 90% and 95% confidence levels for the diameter of an individual bar.

    is this 13.03 +- 1.96(0.63) and 13.03 +- 1.64(0.63) ?

    ii. What proportion of the bars will have a diameter greater than 13.75mm?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tone999 View Post
    A set of metal bars are known to have a mean diameter of 13.03mm with standard deviation of 0.63mm. If it can be assumed that diameters are normally distributed:
    i. find the 90% and 95% confidence levels for the diameter of an individual bar.

    is this 13.03 +- 1.96(0.63) and 13.03 +- 1.64(0.63) ?
    They should be the other way around 13.03 \pm 1.96(0.63) is the 95\% interval and 13.03 \pm 1.64(0.63) the 90\% interval


    ii. What proportion of the bars will have a diameter greater than 13.75mm?
    The z score for 13.75 is:

    z=\frac{13.75-13.03}{0.63}

    which you now look up in the table of the cumulative standard normal distribution and the required probability is 1-P(z).

    CB
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