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 36 kilograms and a standard deviation of 1.56 kilograms. Complete parts a through d below.

a. What is the probability that a filled bag will weigh less than 35.4 kilograms?

The probability is

b. What is the probability that a randomly sampled filled bag will weigh between 35.6 and 38 kilograms?

The probability is

c. What is the minimum weight a bag of dog food could be and remain in the top 14% of all bagsfilled?

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 no more than 3% of all filled bags weigh more than 39 kilograms?

The standard deviation would need to be____kilograms.

(Round to three decimal places asneeded.)