Question: The fill amount of soft drink bottles is normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liters. If bottles contain less than 95% of the listed net content (1.90 liters in this case), the manufacturer may be subject to penalty by the state office of consume affairs. Bottles that have a net content above 2.10 liters may cause excess spillage upon opening. (4 points each)

Suppose that you select a random sample of 25 bottles from this manufacturer. What is the probability that the sample mean \[\bar{X}\] will be between 1.99 liters and 2.01 liters? ________ (Show Work)