The Fallbrook Distributing Company Has a Soft Drink Bottling Plant

question 41

True/False

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.

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Definitions:

Paradox

A statement or proposition that, despite sound reasoning from acceptable premises, leads to a conclusion that seems logically unacceptable or self-contradictory.

Coalition Founder

An individual or entity that initiates the formation of a coalition, which is an alliance among individuals or groups for a common purpose.

Coalition-Building

The process of forming alliances or groups in a strategic manner, often in political contexts or during negotiations, to achieve specific goals.

Need Allocation

The process of determining and distributing resources or responsibilities among parties based on their needs or requirements.