Bayes Theorem

Scenario Script Caption:

Bonnie needs you to investigate some quality control issues at the Burlington factory.

Bonnie: Thanks for coming in. We're working through a problem at our Burlington factory. During a recent spot check of our Fruit Cocktail inventory, the number of defects that we found exceeded our quality standards. That means we had to throw out a good bit of inventory.

Liwei: I am not a happy man. Throwing out inventory is like throwing away money.

Bonnie: Well, that's why we have quality assurance. The way I look at it, we've got an opportunity to improve our quality. Tell me about the Burlington factory. There's a new training initiative that I'd like to test, that could improve our manufacturing processes...

Liwei: Our work force at the Burlington factory is divided into two shifts; a day shift and a night shift. Bonnie: Do we know which one would benefit the most from training?

Caption: The Burlington plant uses two separate work shifts, day shift (8:00 am to 4:30 pm) and night shift (7:00 pm to 3:30 am). The dayshift produces 65% of the product, while the night shift produces the remainder.

Assignment: The Quality Control department said that 8% of the product from the morning shift is defective while 5%. of the night shift product is defective. The Bayes Theorem will help you determine the probability that these defects are an indicator of an underlying quality control issue. Construct a contingency table using the given probabilities and interpret your findings and suggest recommendations.

Answer the following questions using the Bayes Theorem. In your response, make sure that you explain and justify your answers:

1. Given the finished product is defective, what is the probability it was produced during the day shift?

2. What is the probability the finished product was produced during the night shift given it is defective?

Princess Foods has the budget to provide one shift with additional training that should mitigate quality control issues. Should one shift undergo additional training? Use four decimal places.