The Fallbrook Distributing Company has a soft drink bottling plant in Plano, Texas. Based on historical records, if its filling machine is working properly, the mean fill volume per can is 12.0 ounces with a standard deviation equal to 0.13 ounce. Further, the distribution of fill amounts is known to be normally distributed. The State of Texas has a department whose job it is to check on such consumer- related processes as soft drink filling. The idea is to protect the consumer. The department arrives at the Fallbrook plant once a month on an unscheduled day. When they arrive, they randomly select n = 4 cans and carefully measure the volume in each can. If any of these cans contains less than 11.85 ounces, the plant is shut down until a full inspection of the filling process is performed. Based on this information, the probability that the plant will get shut down if it is operating properly is approximately 0.1251.

Question

Quizplus · Accepted Answer

The probability of getting a can with less than 11.85 ounces is 0.1251, which means that the probability of getting a can with at least 11.85 ounces is 1 - 0.1251 = 0.8749. Since the plant is shut down if any of the 4 cans contains less than 11.85 ounces, the probability of the plant getting shut down is 1 - (0.8749)^4 = 0.1251.

The Fallbrook Distributing Company Has a Soft Drink Bottling Plant