Question 3 Suppose that the fill amount of bottles of soft drink has been found to be normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liter. Bottles that contain less...

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Extracted text: Question 3 Suppose that the fill amount of bottles of soft drink has been found to be normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liter. Bottles that contain less than 95 percent of the listed net content (1.90 liters in this case) can result in the manufacturer being subject to a penalty by the state Office of Consumer Affairs, whereas bottles that have a net content above 2.10 liters may cause excess spillage upon opening. What proportion of the bottles will contain Between 1.90 and 2.0 liters? Between 1.90 and 2.10 liters? Below 1.90 liters? Below 1.90 liters or above 2.10 liters? Above 2.10 liters? Between 2.05 and 2.10 liters? 99 percent of the bottles would be expected to contain at least how much soft drink? 99 percent of the bottles would be expected to contain an amount that is between which two values (symmetrically distributed)? Explain the difference in the results in parts g and h. Suppose that in an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler sets the filling machine so that the mean is 2.02 liters. Under these circumstances, what would be your answers in parts a to i? What assumption is critical to your answers in parts a to j?"