Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI u

Question

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 61 kilograms and a standard deviation of 1.05 kilograms. Complete parts a through d below.

a. What is the probability that a filled bag will weigh less than 60.8 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 60.7 and 63 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 8% 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 no more than 2% of all filled bags weigh more than 64 kilograms? The standard deviation would need to be ? kilograms. (Round to three decimal places as needed.)

Explanation / Answer

a)

P(X < 60.8) = P(Z < 60.8 - 61/1.05)

= P(Z < -0.1905)

= 0.4245

b)

P(60.7 < X < 63) = P(X <63) - P(X < 60.7)

= P(Z < 63 - 61/1.05) - P(Z < 60.7-61/1.05)

= P(Z < 1.905) - P(Z < -0.2857)

= 0.9716 - 0.3876

= 0.584

c)

P(X >x) = 8%

=>

x - 61/1.05 = invnorm(1-0.08) = 1.405

x = 62.48

d)

P(X >64) = 2%

=>

64 - 61/s = invnorm(1-0.02) = 2.054

s = 1.46

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