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A machine at Keats Corporation fills 80-ounce detergent jugs. The probability distribution of the amount of detergent in these jugs is normal with a mean

A machine at Keats Corporation fills 80-ounce detergent jugs. The probability distribution of the amount of detergent in these jugs is normal with a mean of 80 ounces and a standard deviation of 0.38 ounce. The quality control inspector takes a sample of 30 jugs once a week and measures the amount of detergent in the jugs in the sample. If the mean of the sample is either less than 79.9 ounces or greater than 80.10 ounces, the inspector concludes that the machine needs an adjustment. What is the probability that based on a sample of 30 jugs the inspector will conclude that the machine needs an adjustment when it actually does not?

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