Prepare a managerial report that addresses the following issues — Great Grasslands Grains Inc GGG manufactures and sells wide variety breakfast cereals

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 I6-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 mea-sure 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 marsh-mallows. 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.

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. y 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 I6-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 live of the sampled boxes fail to meet the standard to .01 or less?

SOLUTION

1. This is a case of binomial experiment consisting of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:

P(X=x) = nCx * Px * (1 - P)n - x

Here the number of trials is number of samples, n = 25

Here, a success is equivalent to that a sample fail to meet the standard weight of banana-flavored marshmallows.

The probability that a sample fail to meet the standard weight of banana-flavored marshmallows if the production process is working properly is 8%. So, P = 0.08

Probability that a weekly sample will result in a shutdown of production if the production process is working properly = Probability that at least 5 boxes out of 25 samples fail to meet the standard weight =

= P(X 5) = 1 - P(X < 5)

So, P(X 5) = 1 - (0.1243 + 0.2703 + 0.2821 + 0.1881 + 0.09) = 0.0452

So, probability that a weekly sample will result in a shutdown of production if the production process is working properly = 0.0452 = 4.52%

2. Now, management wants to shutdown of production if the production process is working properly only for no more than 1%.