Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 9, 8, and 7 for successfully completing the task in the allotted time Assuming that the teams work independently, what is the probability that the task will not be completed in time?

Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 9, 8, and 7 for successfully completing the task in the allotted time Assuming that the teams work independently, what is the probability that the task will not be completed in time?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 44P: You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of...

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At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
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A scientist works in a lab with four summer interns and, as it is the end of the summer, he anticipates the head of the lab will ask him which of them he wants to retain. In terms of quality, the scientist and the head of the lab agree that intern A is better than intern B who is better than intern C who is better than intern D. The scientist would like to keep as many interns as possible and, given any number, the highest-quality ones. However, due to funding restrictions, the head of the lab wants to limit the number of interns that are retained. The head of the lab initially tells the scientist to select two interns to retain. After the scientist chooses two interns, the head of the lab decides whether to allow the scientist to retain a third intern. Thus, the sequence of moves is: 1) the scientist chooses two interns (both of whom are then retained); 2) the head of the lab decides either to allow the scientist to choose a third or not; and possibly 3) if the head of the lab chose…
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's male and female applicants. A random sample of 17 male applicants results in a SAT scoring mean of 1244 with a standard deviation of 59. A random sample of 10 female applicants results in a SAT scoring mean of 1141 with a standard deviation of 34. Using this data, find the 99% confidence interval for the true mean difference between the scoring mean for male applicants and female applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Step 2 of 3: Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to the nearest whole number. Step 3 of 3: Construct the 99% confidence interval. Round your…
Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 0.9, 0.8, and 0.7 for successfully completing the task in the allotted time. Assuming that the teams work independently, what is the probability that the task will not be completed in time? Round your answer to three decimal places.
A company is researching the effectiveness of a new website design to decrease the time to access a website. 32 website users were randomly selected, and their time (in seconds) to access the website with the old and new designs were recorded. The summary statistics for the two sets of data are given in Table Q3-1, and the test results are given in Table Q3-2 and Q3-3. Apply an appropriate hypothesis testing method to test whether the new website design can decrease the time to access the website at the significance level of 5%.
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The management is faced with the problem of choosing one of the products for manufacturing. The probability matrix after market research for the two products was as follows: State of nature Acts Good Fair Poor Product 'A' 0.75 0.15 0.10 Product 'B' 0.60 0.30 0.10 The profits that the management can make for different levels of market acceptability of the products are as follows : Profit (in Rs.) if market is Acts Good Fair Poor 35,000 15,000 5,000 Product 'A' Product 'B' 50,000 20,000 Loss 3,000 Calculate expected value of the choice of alternative and advise the management.
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