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A company that manufactures and bottles apple juice has a machine that automatically fills 16-ounce bottles. There is some variation, however, in the exact amount of juice dispensed into each bottle. From a large number of observations taken over a long period of time, it was found that the actual amount of juice dispensed into each bottle was normally distributed with a mean of 16 ounces and a standard deviation of 1 ounce. Find the percentage of all bottles that are either underfilled or overfilled by at least 0.25 ounce.

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  1. Z = (score-mean)/SD

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score. Remember to calculate for both directions.

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  2. 40.13

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  3. 38.30%

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