A machine at Katz Steel Corporation makes 3-inch-long nails The probability distribution of the leng

A machine at Katz Steel Corporation makes 3-inch-long nails The probability distribution of the lengths of these nails is approximately normal with a mean of 3 inches and a standard deviation of 011 inch The quality control inspector takes a sample of 36 nails once a week and calculates the mean length of these nails If the mean of this sample is either less than 295 inches or greater than 305 inches, the inspector concludes that the machine needs an adjustment What is the probability that based on a sample of 36 nails, the inspector will conclude that the machine needs an adjustment?

Round your answer to 4 decimal places

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