Please provide solutions:

1. Define probability and explain its three perspectives. Provide an example of each.

2. How is the standard normal distribution used to compute normal probabilities?

3. Explain the importance of sampling from a managerial perspective.

4. Explain the central limit theorem. Why is it important in statistical analysis?

5. Explain how a confidence interval changes with changes in the level of confidence and sample size.

6. Explain the difference between the null hypothesis and alternative hypothesis. Which one can be proven in a statistical sense?

7. How can you determine when to use a lower one-tailed test of hypothesis versus an upper one-tailed test?

8. Explain the purpose of the chi-square test for independence. Provide some practical examples where this test might be used in business.

9. Explain the difference between simple and multiple linear regression.

10. Explain what is the coefficient of determination, R^2 (R-squared)? What does it measure?

11. Summarize statistical methods used in forecasting and the types of time series to which they are most appropriate.

12. Summarize some of the practical issues in using forecasting tools and approaches.

13. Describe the steps involved in applying statistical process control.

14. List the principal rules for examining a control chart to determine if the process is in control.

15. What is process capability? How is it measured?

16. What is a decision model, and what are the three types of inputs common to decision models?

17. Describe how to use Excel data tables, Scenario Manager, and goal seek tools to analyze decision models.

18. Explain basic spreadsheet approaches for implementing decision models in Excel.

19. Explain the concept of risk analysis and how Monte Carlo simulation can provide useful information for making decisions.

20. Summarize the modeling and analysis using Solver tool available in Excel and what information it provides. You need to discuss the steps to run optimization using Solver in excel and produce optimization output and sensitivity reports.

21. Describe the types of decisions that do not involve uncertainty and risk and common approaches used for analyzing them.

22. Explain how payback period, NPV, and IRR criteria are used in decision making.

23. Explain the components of a decision tree and how optimal decisions are computed.

24. Describe the three elements that all queuing systems have in common.

25. List and define the major types of performance measures used in queuing analysis.