# solution

Great Grasslands Grains (GGG), the manufacturer of Go Bananas! cereal, has discovered that their customers are enthusiastic about the cereal when the 16-ounce box contains between 1.6 ounces and 2.4 ounces of banana flavored marshmallows. Because the company wants to stay within that limit, it randomly samples 25 boxes each week to ensure this metric is met. The production line shuts down for inspection if too many boxes fail the inspection. GGG states that only 8% of boxes fail to meet the standard, but they decide to shut down the plant if more than 5 of 25 boxes fail. This was calculated using the Binomial Probability of Distribution method because it met all four properties of a binomial experiment: The experiment consisted of a sequence of n identical trials There were only two outcomes (meets standards and does not meet standards) The probability of success remains constant between trials The trials are independent All calculations were done in Excel and are attached. The probability that a weekly sample will result in a shutdown if the process is working properly is 4.514%. Their current policy is to shut the production lines down when 5 of 25 boxes, or 20% of boxes fail. The companyâ€™s policy will result in few shutdowns, especially since the current rate of weight failures is 8%. The company wants to shut down production no more than 1% of the time when processes are working properly. In this case, at least 7 boxes must fail QA checks before shutdown will occur. The VP of production would like to redesign the production process to reduce the percentage of boxes that fail to meet standards. It should be redesigned so that only between 5 and 6% of boxes fail to meet standard, rather than the usual 8% that exists today. There are a lot of industries that use production quality assurance tests, and the one closest to my profession would be drug manufacturers. They have strict QA specifications that they need to follow. While I donâ€™t use these types of tests in my current work, I can see the benefit of it in many industries.

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