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    Bumper Installation

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    The time taken to install bumpers on cars passing through a particular assembly line is normally distributed with mean time u=2.00 minutes and standard deviation =36 minutes. A sample on n=100 is obtained and a mean bumper installation time X-bar will be calculated.
    1. Find the value of standard deviation X bar.
    Determine the probability that Xbar will
    2. Lie between 2.07 and 1.93
    3. Exceed 1.98 minutes
    4. Fall below 1.94
    5. Lie between 2.02 and 2.08
    6. Fall above 2.05

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    Solution Preview

    I doubt the standard deviation of 36 minutes, which is even far higher than the mean value. Because the Sm of sample is Sd/SQRT(N)=36/SQRT(100)=3.6 minutes, then the answer to 1~6 will all be 100%.
    Therefore, I think it might be 0.36 minute or 36 seconds, but it can't be decided from your working (it's not clear how you reach 0.27)
    However, I'll take 0.36 minute as the standard deviation. If the true value is 36 seconds=36/60=0.6 minute, you only need to replace standard deviation with 0.6 minute and finish the calculation as ...

    Solution Summary

    The solution discusses the time taken to install bumpers on cars passing through a particular assembly line is normally distributed with mean time u=2.00 minutes and standard deviation =36 minutes. A sample on n=100 is obtained and a mean bumper installation time X-bar will be calculated.
    1. Find the value of standard deviation X bar.
    Determine the probability that Xbar will
    2. Lie between 2.07 and 1.93
    3. Exceed 1.98 minutes
    4. Fall below 1.94
    5. Lie between 2.02 and 2.08
    6. Fall above 2.05

    $2.49

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