Scenario:A major city must decide between two competing projects to address increasing traffic congestion: expanding the existing subway system (high cost, long-term) or implementing a high-speed bus network (lower cost, faster implementation).The mayor’s decision is influenced by values regarding environmental impact, budget constraints, and equitable access. However, future ridership is highly uncertain due to shifting remote work trends. Initial projections estimate the subway will cost $2 billion over 10 years, while the bus network will cost $500 million over 5 years.Question:Apply the principles of Decision Analysis to develop a strategic recommendation for the city. In your response, address the following:Objective Formulation: Distinguish the mayor’s fundamental objectives from potential means objectives in this specific decision context.Determine the Horizon for the decision model.Sensitivity Analysis: Explain how sensitivity analysis should be applied and to which uncertainty(ies) it should be applied.

We know that the silicon wafers produced by a certain machine have an average of 2 defects per square centimeter.  We wish to calculate the probability that there will be more than 15 defects in a ten square centimeter silicon wafer produced by this machine.  In order to calculate that probability, we should use which of the following distributions?

Which approach to probability defines the probability of an event as an individual’s “degree of belief” in the occurrence of that event?

Define a requisite decision model as discussed in our class. What are two factors that contribute to the convergence of such a model, and at what point should a decision maker stop adding new elements to their analysis?

Briefly define what makes a decision model requisite.

Consider the following decision tree: dt1.png The above tree has how many decision paths? [BLANK-1]

An appliance dealer sells three different models of upright freezers having 12, 17, and 21 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has the following pmf  x 12 17 21 p(x) 0.2 0.3  0.5 Answer the following; round your answers to 2 decimal places as needed. a) The expected value of the storage capacity of the freezer that the next customer purchases is [BLANK-1] cubic feet. b) The variance of the storage capacity of the freezer that the next customer purchases is [BLANK-2] cubic feet.

To prevent undue political influence, US Supreme Court justices serve until they either 1) choose to retire, or 2) reach the end of their natural life. The justices.csv file (from Lab 3, in our shared data folder) contains information about each US Supreme Court justice appointed in the history of the country. To review, the columns of the file contain: Justice first name Justice last name State the justice is from Name of the president who appointed the justice Year appointed Year the appointment ended The 6th column contains 0 for justices currently serving at the time the data file was compiled. Write a function named three_longest_appts that accepts three arguments: a file name, a beginning year, and an ending year. Return a pandas dataframe containing all data columns for the three longest-serving justices appointed between the beginning year and ending year (inclusive). Include in your analysis only those justices whose term has ended (retired or passed away). For full credit, your function should use pandas concepts and techniques to calculate and return the result without using loops or list comprehensions. In [1]: three_longest_appts(‘justices.csv’, 1789, 2022) Out[1]: first last state pres beg end term 43 John Harlan KY Rutherford B. Hayes 1877 1971 94 31 William Douglas CT Franklin D. Roosevelt 1939 1975 36 90 John Stevens IL Gerald R. Ford 1975 2010 35 In [2]: three_longest_appts(‘justices.csv’, 1789, 1905) Out[2]: first last state pres beg end term 43 John Harlan KY Rutherford B. Hayes 1877 1971 94 61 John Marshall VA John Adams 1801 1835 34 34 Stephen Field CA Abraham Lincoln 1863 1897 34 In [3]: three_longest_appts(‘justices.csv’, 1906, 2022) Out[3]: first last state pres beg end term 31 William Douglas CT Franklin D. Roosevelt 1939 1975 36 90 John Stevens IL Gerald R. Ford 1975 2010 35 4 Hugo Black AL Franklin D. Roosevelt 1937 1971 34 In [4]: three_longest_appts(‘justices.csv’, 1964, 2022) Out[4]: first last state pres beg end term 90 John Stevens IL Gerald R. Ford 1975 2010 35 80 William Rehnquist VA Ronald Reagan 1972 2005 33 56 Anthony Kennedy CA Ronald Reagan 1988 2018 30

Which of the following people is considered highly compensated for 2025?

Jared, age 54, earns $300,000 per year and is a participant in his employer’s 401(k) plan. Ignoring the ADP Test requirements, what is the maximum amount that Jared can defer under the 401(k) plan in 2025?