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 32 kilograms and a standard deviation of 1.32 kilograms. Complete parts a through d below. a. What is the probability that a filled bag will weigh less than 31.6 kilograms? The probability is. (Round to four decimal places as needed.) b. What is the probability that a randomly sampled filled bag will weigh between 30.5 and 34 kilograms? The probability is . (Round to four decimal places as needed.) c. What is the minimum weight a bag of dog food could be and remain in the top 16% of all bags filled? The minimum weight is kilograms. (Round to three decimal places as needed.) d. 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 9% of all filled bags weigh more than 36 kilograms? The standard deviation would need to be ☐kilograms. (Round to three decimal places as needed.)

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