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Statical Data in a Business - Essay Example

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This paper will involve use of Bayes’ theorem to establish the cost of defective products that are produced by the two plants of a detergent producing company, one located in Florida and the other one in Texas. Bayes theorem, therefore, will be used to make decision in…
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Statical Data in a Business
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Download file to see previous pages A central depot is set up, where all the detergent that is manufactured by the two plants is sent and mixed together. Following a careful investigation, the production manager established that 10% of the detergent manufactured in Florida and 5% of the detergent manufactured in Texas is faulty and hence cannot be used. It is also known that when the company sells faulty products, its goodwill is tainted and the cost of replacing the faulty product is high. The production manager finds it prudent to allocate these costs reasonably between the two production facilities. This allocation requires knowledge of the probability that a particular production line will produce faulty detergent. In particular, the production manager should seek answers to the following questions:
To find the solution to this problem, a probability function is constructed, whereby, F stands for the event that a unit of detergent is faulty. In other words, the production manager is aware of the following?
It is by now known that 40% of the detergent is produced by Florida plant and 60% from Texas. As such, P (Florida) = 0.40 and P (Texas) = 0.6. Using Bayes’ Theorem, the following probability from each production line is presented:
These probabilities imply that 57.14% of the faulty cost should be assigned to the Florida plant and 42.86% assigned to the Texas plant. It is notable that P (F) represents the probability of the faulty detergent. This probability can be represented as follows:
The production manager has applied Bayes’ theorem to craft a fair method of allocation cost that is associated with production of defective products between the two production facilities (Peebles, 1993). Although the production manager was not certain of the exact cost that comes from each plant, the probabilities have been formed devoid of bias. Therefore, the company will be more decisive when allocating these costs between ...Download file to see next pagesRead More
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