CompetencyGiven a real-life application, develop a confidence interval for a population parameter and its interpretation.InstructionsScenario (information repeated for deliverable 01, 03, and 04)A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:A listing of the jobs by titleThe salary (in dollars) for each jobYou have previously explained some of the basic statistics to your client already, and he really liked your work. Now he wants you to analyze the confidence intervals.Background information on the DataThe data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.What to SubmitYour boss wants you to submit the spreadsheet with the completed calculations, answers, and analysis.

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For this Critical Thinking Assignment, you will be creating your own real-world scenario and exploring the meaning of differentiation of exponential functions in that context. Complete the following steps:Select a real-world scenario that can be modeled by an exponential function and define the function F(x) based on your scenario. (Ex.: Suppose that F(x) computes the rabbit population on a game reserve that doubles every 6 months. Suppose there were 120 rabbits initially.)Write a mathematical expression for F(x).Find the domain and range of F(x).Find F(x) and F '(x) at any point.Find all x values for which F '(x) = 0.Based on your work in Part I, discuss the following:Discuss if your function F(x) is differentiable and why. If it is not differentiable, select another function that is and discuss the change you made.Discuss the domain and range of F(x) and why they make sense in the context of your problem.Discuss the physical meaning of F(x) and F '(x) at a point in the context of your problem.Discuss what it means for F '(x) = 0 in the context of your problem.Reflect on any adjustments you had to make to your original problem context and discuss what characteristics of a real-world context make it a valid choice for applying differentiation concepts to it.Provide at least two other real-world situations where differentiation can be applied and respond to the following:What common characteristics do the real-world scenarios you chose share?What did you look for in the way that the real-world scenario can be modeled?Discuss the criteria for selecting a real-world scenario that would change if you were seeking to model it with a logarithmic function instead. What key similarities and differences would you find?