Final Exam Points possible: 100 PREDICT 401: Introduction to Statistical Analysis Description: The final exam will cover topics from sessions 1-9. Resources: The exam is completely open book. You may use course textbooks, materials provided on Canvas, or basic graphing calculators (such as TI 83 or 84). Any more advanced calculators, Excel Solver, Web calculators, Web-graphic calculators, or simplex method calculators are not allowed. Programming languages other than Python are also not permitted. For questions that require calculations, all calculations should be shown, not just the final answer. This will allow for partial credit for those answers that might be set up correctly but have calculation errors. For questions that specifically require Python, the code and output should be included with your answer. For questions that require graphs, only use Python. Restrictions: All answers are to be your work only. You are not to receive assistance from any other person. To complete the exam: 1. Answer all questions on the exam thoroughly. Create a Microsoft Word document, including the question number, the question, your typed answer, and graphs if required. You may use Word's equation editor to complete your answers. 2. Once you have completed your exam, return to the exam item where you downloaded the exam PDF, click View/Complete Assignment, and submit your document. 1. A patient takes vitamin pills daily. Each day he must have at least 240 IU of vitamin A, 5 mg of vitamin B1, and 120 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 1 mg of vitamin B1, and 15 mg of vitamin C; and pill 2, which contains 30 IU of vitamin A, 1 mg of vitamin B1, and 40 mg of vitamin C. Pill 1 costs $0.10, and pill 2 costs $0.20. Using Python, determine how many of each pill he should take daily in order to minimize cost and determine the minimum cost. Also, determine the amount of surplus of each type of vitamin, if any. 2. A recent survey found that 86% of first-year college students were involved in volunteer work at least occasionally. Suppose a random sample of 13 college students is taken. Find the probability that at least 10 students volunteered at least occasionally. 3. The following is a graph of a third degree polynomial with leading coefficient 1. Determine the function depicted in the graph. Using Python, recreate the graph of the original function, (), as well as the graph of its derivative. 4. The average number of vehicles waiting in line to enter a parking ramp can be modeled by the function () = 2 2(1 ) where x is a quantity between 0 and 1 known as the traffic intensity. Find the rate of change of the number of vehicles in line with respect to the traffic intensity for x = 0.3. 5. Using Wired magazine as our resource, we constructed the mathematical model = 100 0.0482 for the percentage of Samsung phones still un use after years. Using Python, determine the rate of change of the percent of phones still being used after 5 years. 6. For the following function, determine the domain, critical points, intervals where the function is increasing or decreasing, inflection points, intervals of concavity, intercepts, and asymptotes where applicable. Use this information to graph the function. () = 5 15 7. The number of diseased cells () at time increases at a rate () = , where is the rate of increase at time 0 (in cells per day) and is a constant. Suppose = 40, and at 6 days, the cells are growing at a rate of 120 per day. Find a formula for the number of cells after days, given that 200 cell are present at = 0. Determine the number of cells present after 16 days. 8. For a certain Samsung phone, the rate of sales in millions of units per hour is given by () = 3 5 + +1 +1 where is time (in hours) after the phone first goes on sale. Find the total sales of the phone from 8 to 24 hours after it is goes on sale. 9. Show that the following function is a probability density function on (0, ]. 3 , 0 2 () = { 12 16 , > 2 4 Determine (1 5). 10. The time between goals (in minutes) for a professional soccer team during a recent season can be approximated by () = 1 85 85 Using Python determine the (separate) probabilities that the time for a goal is no more than 68 minutes, and 457 minutes or more