Great Grasslands Grains, Inc. (GGG) manufactures and sells a wide variety of breakfast cereals. GGG’s product development lab recently created a new cereal that consists of rice flakes and banana-flavored marshmallows. The company’s marketing research department has tested the new cereal extensively and has found that consumers are enthusiastic about the cereal when 16-ounce boxes contain at least 1.6 ounces and no more than 2.4 ounces of the 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 or more than 2.4 ounces of banana-flavored marshmallows in each 16-ounce box of Go Bananas! Tina Finkel, VP of Production for GGG, has suggested that the company measure the weight of banana-flavored marshmallows in a random sample of 25 boxes of Go Bananas! on a weekly basis. Each week, GGG 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 Go Bananas! fail to meet the standard weight of banana-flavored marshmallows. After much debate, GGG management has decided to shut down production of Go Bananas! if at least five boxes in a weekly sample fail to meet the standard weight of banana-flavored marshmallows.
Managerial Report
Prepare a managerial report that addresses the following issues.
- 1. Calculate the
probability that a weekly sample will result in a shutdown of production if the production process is working properly. Comment on GGG management’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 than 1% of the time when the production process is working properly. Suggest the appropriate number of boxes in the weekly sample that must fail to meet the standard weight of banana-flavored marshmallows in order for production to be shut down if this goal is to be achieved.
- 3. Ms. Finkel has suggested that if given sufficient resources, she could redesign the production process to reduce the percentage of 16-ounce boxes of Go Bananas! that fail to meet the standard weight of banana-flavored marshmallows when the process is working properly. To what level must Ms. Finkel reduce the percentage of 16-ounce boxes of Go Bananas! that fail to meet the standard weight of banana-flavored marshmallows when the process is working properly in order for her to reduce the probability at least five of the sampled boxes fail to meet the standard to .01 or less?
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Chapter 5 Solutions
Essentials of Statistics for Business and Economics (with XLSTAT Printed Access Card)
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- A local fast-food restaurant serves buffalo wings. The restaurant’s managers notice that they normally sell the following proportions of flavors for their wings: 20% Spicy Garlic, 30% Classic Medium, 20% Teriyaki, 20% Hot BBQ, and 10% Asian Zing. After running a campaign to promote their nontraditional specialty wings, they want to know if the campaign has made an impact. The results after 10 days are listed in the following table. Is there sufficient evidence at the 0.025 level of significance to say that the promotional campaign has made any difference in the proportions of flavors sold? Buffalo Wing Sales Number Sold Spicy Garlic 100 Classic Medium 146 Teriyaki 109 Hot BBQ 108 Asian Zing 73 Step 3 of 4: Compute the value of the test statistic. Round any intermediate calculations to at least six decimal places, and round your final answer to three decimal placesarrow_forwardA local fast-food restaurant serves buffalo wings. The restaurant’s managers notice that they normally sell the following proportions of flavors for their wings: 10% Spicy Garlic, 20% Classic Medium, 30% Teriyaki, 20%Hot BBQ, and 20% Asian Zing. After running a campaign to promote their nontraditional specialty wings, they want to know if the campaign has made an impact. The results after 10 days are listed in the following table. Is there sufficient evidence at the 0.005 level of significance to say that the promotional campaign has made any difference in the proportions of flavors sold? Buffalo Wing Sales Number Sold Spicy Garlic 74 Classic Medium 111 Teriyaki 141 Hot BBQ 100 Asian Zing 103 Copy Data Step 4 of 4 : Draw a conclusion and interpret the decision.arrow_forwardA local fast-food restaurant serves buffalo wings. The restaurant's managers notice that they normally sell the following proportions of flavors for their wings: 10 % Spicy Garlic, 30 % Classic Medium, 20 % Teriyaki, 20 % Hot BBQ, and 20 % Asian Zing. After running a campaign to promote their nontraditional specialty wings, they want to know if the campaign has made an impact. The results after 10 days are listed in the following table. Is there sufficient evidence at the 0.005 level of significance to say that the promotional campaign has made any difference in the proportions of flavors sold? Buffalo Wing Sales Number Sold Spicy Garlic 76 Classic Medium 142 Teriyaki 114 Hot BBQ 122 Asian Zing 109 Copy Data Step 2 of 4: Calculate the expected value for the number of classic medium wings sold. Round your answer to three decimal places, if necessary.arrow_forward
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