Great Grasslands Grains, Inc. (GGG) manufactures and sells a wide variety of breakfastcereals. GGG's product development lab recently created a new cereal that consists of riceflakes and banana-flavored marshmallows. The company's marketing research departmenthas tested the new cereal extensively and has found that consumers are enthusiastic aboutthe cereal when 16-ounce boxes contain at least 1.6 ounces and no more than 2.4 ounces ofthe banana-flavored marshmallows.As GGG prepares to begin producing and selling 16-ounce boxes of the new cereal,which it has named Go Bananas!, management is concerned about the amount of banana-flavored marshmallows. It wants to be careful not to include less than 1.6 ounces ormore than 2.4 ounces of banana-flavored marshmallows in each 16-ounce box of GoBananas!. Tina Finkel, VP of Production for GGG, has suggested that the company mea-sure the weight of banana-flavored marshmallows in a random sample of 25 boxes ofGo Bananas! on a weekly basis. Each week, GGG can count the number of boxes outof the 25 boxes in the sample that contain less than 1.6 ounces or more than 2.4 ouncesof banana-flavored marshmallows; if the number of boxes that fail to meet the standardweight of banana-flavored marshmallows is too high, production will be shut down andinspected.Ms. Finkel and her staff have designed the production process so that only 8% of all16-ounce boxes of Go Bananas! fail to meet the standard weight of banana-flavored marsh-mallows. After much debate, GGG management has decided to shut down production ofGo Bananas! if at least five boxes in a weekly sample fail to meet the standard weight ofbanana-flavored marshmallows. Prepare a managerial report that addresses the following issues.1. Calculate the probability that a weekly sample will result in a shutdown of produc-tion if the production process is working properly. Comment on GGG manage-ment's policy for deciding when to shut down production of Go Bananas!.2. GGG management wants to shut down production of Go Bananas! no more than1% of the time when the production process is working properly. Suggest the ap-propriate number of boxes in the weekly sample that must fail to meet the standardweight of banana-flavored marshmallows in order for production to be shut downif this goal is to be achieved.3. Ms. Finkel has suggested that if given sufficient resources, she could redesign the pro-duction process to reduce the percentage of 16-ounce boxes of Go Bananas! that fail tomeet the standard weight of banana-flavored marshmallows when the process is work-ing properly. To what level must Ms. Finkel reduce the percentage of 16-ounce boxesof Go Bananas! that fail to meet the standard weight of banana-flavored marshmal-lows when the process is working properly in order for her to reduce the probabilityat least five of the sampled boxes fail to meet the standard to .01 or less?

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