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20 August, 13:27

Smith is a weld inspector at a shipyard. he knows from keeping track of good and substandard welds that for the afternoon? shift, 5% of all welds done will be substandard. if smith checks 300 of the 7500 welds completed that? shift, would it be unusual for smith to find 30 or more substandard? welds?

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  1. 20 August, 13:43
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    The probability of finding a substandard weld is: p = 5% = 0.05

    We are given that the sample size: n = 300

    Using the Poisson Distribution, the average number of welds (m) is:

    m = n*p =

    m = 300 * 0.05

    m = 15

    The standard deviation of welds (s) is calculated by:

    s = sqrt (m)

    s = sqrt (15)

    s = 3.873

    Assuming normal distribution, the z value corresponding to 30 sub standards is:

    z = (X - Mean) / standard deviation

    z = (30 - 15) / 3.873

    z = 15 / 3.873

    z = 3.87

    The z value based on the standard normal curves has a maximum value of 3.49. Beyond that z value of 3.49 would mean exceeding 100%. Therefore z = 3.87 is not normal and definitely it is unusual to find 30 or more substandard.
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