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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 0.035 ounce. Operations managers at 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 11.97 and 12.03 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? The probability is 0.6086. (Round to four decimal places as needed.) b. Assume that the manager is focused on an upcoming audit by the Department of Weights and Measures. She knows the process is to select one can at random and that if it contains less than 11.96 ounces, the company will be reprimanded and potentially fined. Assuming that the manager wants at most a 5% chance of this happening, at what level should she set the mean fill level? Comment on the ramifications of this step, assuming that the company fills tens of thousands of cans each week. Set the mean fill level at ounces. (Round to two decimal places as needed.)

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 0.035 ounce. Operations managers at 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 11.97 and 12.03 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? The probability is 0.6086. (Round to four decimal places as needed.) b. Assume that the manager is focused on an upcoming audit by the Department of Weights and Measures. She knows the process is to select one can at random and that if it contains less than 11.96 ounces, the company will be reprimanded and potentially fined. Assuming that the manager wants at most a 5% chance of this happening, at what level should she set the mean fill level? Comment on the ramifications of this step, assuming that the company fills tens of thousands of cans each week. Set the mean fill level at ounces. (Round to two decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 4CYU
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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 0.035 ounce. Operations managers at 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 11.97 and 12.03 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? The probability is 0.6086. (Round to four decimal places as needed.) b. Assume that the manager is focused on an upcoming audit by the Department of Weights and Measures. She knows the process is to select one can at random and that if it contains less than 11.96 ounces, the company will be reprimanded and potentially fined. Assuming that the manager wants at most a 5% chance of this happening, at what level should she set the mean fill level? Comment on the ramifications of this step, assuming that the company fills tens of thousands of cans each week. Set the mean fill level at ounces. (Round to two decimal places as needed.)
Transcribed Image Text: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 0.035 ounce. Operations managers at 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 11.97 and 12.03 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? The probability is 0.6086. (Round to four decimal places as needed.) b. Assume that the manager is focused on an upcoming audit by the Department of Weights and Measures. She knows the process is to select one can at random and that if it contains less than 11.96 ounces, the company will be reprimanded and potentially fined. Assuming that the manager wants at most a 5% chance of this happening, at what level should she set the mean fill level? Comment on the ramifications of this step, assuming that the company fills tens of thousands of cans each week. Set the mean fill level at ounces. (Round to two decimal places as needed.)
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