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

39

kilograms and a standard deviation of

0.96

kilograms. Complete parts a through d below.

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

38.9

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

36.9

and

40

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

10%

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

10%

of all filled bags weigh more than 43 kilograms?

The standard deviation would need to be ___ kilograms.

(Round to three decimal places as needed.)