Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 49 kilograms and a standard deviation of 1.84 kilograms. DNI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 10% of all filled bags weigh more than 54 kilograms? (Round to three decimal places as needed)

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 49 kilograms and a
standard deviation of 1.84 kilograms. DNI is unable to adjust the mean of the filling process, However it is able to adiust the standard deviation of the filling process. What would the standard deviation need to be so that no more than
10% of all filled bags weigh more than 54 kilograms? (Round to three decimal places as needed)
Transcribed Image Text:Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 49 kilograms and a standard deviation of 1.84 kilograms. DNI is unable to adjust the mean of the filling process, However it is able to adiust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 10% of all filled bags weigh more than 54 kilograms? (Round to three decimal places as needed)
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