A bottling plant fills 12-ounce cans of soda by an automated filling process that can be adjusted to any mean fill volume and that will fill cans according to a normal distribution. However, not all cans will contain the same volume due to variation in the filling process. Historical records show that regardless of what the mean is set at, the standard deviation in fill will be 0. 125 ounce. Operations managers of the plant know that if they put too much soda in a can, the company loses money If too little is put in the can, customers are short changed, and the State Department of Weights and Measures may fine the company Complete parts a and b below a. Suppose the industry standards for fill volume call for each 12 ounce can to contain between 11.88 and 12.12 ounces. Assuming that the manager sets the mean fill at 12 ounces, what is the probability that a can will contain a volume of product that falls in the desired range? I he probability is 0.G629. (lound to tour decimal places as needed.) to Assume that the manager is focused on an upcoming audit by the Department of Weights and Mexesmes She knows the proces is to sekad one caan al random and that if il contains less than 11 87 ounces, the company will be reprimanded and potentially fined Assuming that the manage wants al most a 5% chance of this happening, al what level should she set the mean fill level? Comment on the ramifications of this stop, assuming that the company fills tons of thousands of canes each week Set the mean fil level at ounces. (Round to two decimal places as needed.)