The Aberdeen CocaCola Bottling plant located in Aberdeen NC

The Aberdeen Coca-Cola Bottling plant located in Aberdeen, NC, is the bottler and distributer for Coca-Cola products in the area. The product line includes 12-ounce cans of Coke products. The cans are filled by an automated process that will fill cans according to a normal distribution with a standard deviation of 0.035 ounces. The default mean fill rate is 12-ounces, but it can be adjusted to any mean fill volume. Operations managers at the plant know that if they put too much Coke in a can, the company loses money. If they put less than 11.97 ounces in a can, the NC Department of Weights and Measures (NCWM) fines the company.

(a) The procedure of NCWM is to select a can at random and measure the volume of Coke in that can. Suppose that the managers set the mean fill rate at its default value, 12 ounces. What is the probability that the company will be fined by NCWM? Plot the probability density function for the automated system and shade the area that corresponds to this probability.

(b) Suppose that the manager wants to keep the probability of being fined at 5%. At what level should the manager set the mean fill rate? Plot the probability density function for the automated system and shade the area that corresponds to this probability. (c) Suppose that the internal audit department penalizes the manager if they fill more than 12.05 ounces in a can and they also select a can at random and measure the volume of Coke in that can. Suppose that the manager sets the mean fill rate at its default value 12 ounces. What is the probability that neither the company is fined by NCWM nor the manager is penalized? Plot the probability density function for the automated system and shade the area that corresponds to this probability.

(d) Briefly comment on whether the manager can increase the probability in part (c) by changing the mean fill rate. You may plot the probability density function for the automated system to explain your answer.

Solution