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Hemmingway, Inc., is considering starting a research and development (R&D) project at an initial cost of $5 million. Profit projections appear promising, but the company's president is concerned because the probability that the R&D project will be successful is only 0.5. Secondly, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized (0.5 chance of high demand, with a projected outcome of $59 million; 0.3 chance of medium demand, with a projected outcome of $45 million; 0.2 chance of low demand, with a projected outcome of $35 million). Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million facility.
a. Build a decision tree (DT) for this problem.b. Analyze the DT to determine the optimal strategy for the company. What is the expected value of the optimal strategy?c. What must be the selling price for the company to consider selling the rights to the product?d. Develop a risk profile for the optimal strategy.
You are investigating the flight characteristics of different kinds of birds. You collect a sample of 33 European swallows (Hirundo rustica) and measure their air-speed velocity in a borrowed wind tunnel.
Show that if the roots of the polynomial p are all real, then the roots of p' are all real. If, in addition, the roots of p are all simple, then the roots of p' are all simple.
The percentage rates of home ownership for 8 randomly selected states are listed below. Estimate the population variance and standard deviation for the percentage rate of home ownership with 99% confidence level.
Identical parts of which 10 are defective and 90 are non-defective. Three parts are selected without replacement. What is the probability that at least one part is defective?
Using one proportion z test to find whether or not to support the claim - There is little evidence to reject H 0 , therefore they conclude the tvs are 20 pounds on average.
Suppose you take a random sample of 15 bearings and compute xbar = 8.2535. What is the probability that you will see a sample mean greater than xbar?
The data below are the numbers of hours of homework done as reported by 24 high school juniors for the last week in September 2006.
Find an unbiased estimator of mp(1 - p)/n. Find the optimal estimator using the Rao-Blackwell Theorem.
Determine the probability that we would reject null hypothesis given that it is true?
Determine mean and standard deviation for number of erroneous returns per batch.
The sample yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounces. Use a 0.05 level of significance and test to see if the machine is in perfect adjustment (perform all six steps of hypothesis testing, including p-values)..
A contractor is considering a sale that promises a profit of $37,000 with a probability of 0.7 or a loss of (due to bad weather and such) of $18,000 with a probability of 0.3. What is the expected profit?
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