As GM prepares to begin producing and selling 16-ounce boxes of the new cereal, which it has named Cheerios, management is concerned about the amount of banana-flavored marshmallows. It wants to be careful not to include less than 1.6 ounces or more than 2.4 ounces of banana flavored marshmallows in each 16-ounce box of Cheerios. Tina Finkel, VP of Production for GM, has suggested that the company measure the weight of banana-flavored marshmallows in a random sample of 25 boxes of Cheerios on a weekly basis. Each week GM can count the number of boxes out of the 25 boxes in the sample that contain less than 1.6 ounces or more than 2.4 ounces of banana-flavored marshmallows; if the number of boxes that fail to meet the standard weight of banana-flavored marshmallows is too high, production will be shut down and inspected. Ms. Finkel and her staff have designed the production process so that only 8% of all 16-ounce boxes of Cheerios fail to meet the standard weight of banana-flavored marshmallows. After much debate, GM management has decided to shut down production of Cheerios if at least five boxes in a weekly sample fail to meet the standard weight of banana-flavored marshmallows. Calculate the probability that a weekly sample will result in a shutdown of production if the production process is working properly
As GM prepares to begin producing and selling 16-ounce boxes of the new cereal, which it has named Cheerios, management is concerned about the amount of banana-flavored marshmallows. It wants to be careful not to include less than 1.6 ounces or more than 2.4 ounces of banana flavored marshmallows in each 16-ounce box of Cheerios. Tina Finkel, VP of Production for GM, has suggested that the company measure the weight of banana-flavored marshmallows in a random sample of 25 boxes of Cheerios on a weekly basis. Each week GM can count the number of boxes out of the 25 boxes in the sample that contain less than 1.6 ounces or more than 2.4 ounces of banana-flavored marshmallows; if the number of boxes that fail to meet the standard weight of banana-flavored marshmallows is too high, production will be shut down and inspected.
Ms. Finkel and her staff have designed the production process so that only 8% of all 16-ounce boxes of Cheerios fail to meet the standard weight of banana-flavored marshmallows. After much debate, GM management has decided to shut down production of Cheerios if at least five boxes in a weekly sample fail to meet the standard weight of banana-flavored marshmallows.
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