The Fallbrook Distributing Company Has a Soft Drink Bottling Plant

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 ounces.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 0.4141.