The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, a dairy bottles milk in 1-litre containers. Suppose that if the filling process is working correctly, the mean weight of all containers is 1.00 litre with a standard deviation equal to 0.10 litres. Assume that the population of fill volumes is normally distributed. The department's test process requires that they select a random sample of n = 9 containers. If the sample mean is less than 0.97 litres, the department will fine the dairy. Based on this information, what is the probability that the dairy will get fined even when its filling process is working correctly?

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• Use the tables in your text
• Report the answer in the space provided to four (4) decimal places