A company is considering whether to market a newproduct. Assume, for simplicity, that if this product ismarketed, there are only two possible outcomes: successor failure. The company assesses that the probabilitiesof these two outcomes are p and 1 2 p, respectively. Ifthe product is marketed and it proves to be a failure, thecompany will have a net loss of $450,000. If the productis marketed and it proves to be a success, the company will have a net gain of $750,000. If the companydecides not to market the product, there is no gain orloss. The company can first survey prospective buyersof this new product. The results of the consumer surveycan be classified as favorable, neutral, or unfavorable.Based on similar surveys for previous products, thecompany assesses the probabilities of favorable, neutral,and unfavorable survey results to be 0.6, 0.3, and 0.1for a product that will eventually be a success, and itassesses these probabilities to be 0.1, 0.2, and 0.7 for aproduct that will eventually be a failure. The total cost ofadministering this survey is C dollars.a. Let p 5 0.4. For which values of C, if any, would thiscompany choose to conduct the survey?b. Let p 5 0.4. What is the largest amount this company would be willing to pay for perfect information about the potential success or failure of thenew product?c. Let p 5 0.5 and C 5 $15,000. Find the strategythat maximizes the company’s expected net earnings. Does the optimal strategy involve conductingthe survey? Explain why or why not.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A company is considering whether to market a new
product. Assume, for simplicity, that if this product is
marketed, there are only two possible outcomes: success
or failure. The company assesses that the probabilities
of these two outcomes are p and 1 2 p, respectively. If
the product is marketed and it proves to be a failure, the
company will have a net loss of $450,000. If the product
is marketed and it proves to be a success, the company will have a net gain of $750,000. If the company
decides not to market the product, there is no gain or
loss. The company can first survey prospective buyers
of this new product. The results of the consumer survey
can be classified as favorable, neutral, or unfavorable.
Based on similar surveys for previous products, the
company assesses the probabilities of favorable, neutral,
and unfavorable survey results to be 0.6, 0.3, and 0.1
for a product that will eventually be a success, and it
assesses these probabilities to be 0.1, 0.2, and 0.7 for a
product that will eventually be a failure. The total cost of
administering this survey is C dollars.
a. Let p 5 0.4. For which values of C, if any, would this
company choose to conduct the survey?
b. Let p 5 0.4. What is the largest amount this company would be willing to pay for perfect information about the potential success or failure of the
new product?
c. Let p 5 0.5 and C 5 $15,000. Find the strategy
that maximizes the company’s expected net earnings. Does the optimal strategy involve conducting
the survey? Explain why or why not.
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