91ffx - ADM 2303 Final Examination Professors Nash, Quon,...

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ADM 2303 Final Examination Fall 1991 Time: 3 Hours Professors Nash, Quon, Kuttner NAME: STUDENT NUMBER: PROFESSOR: Nash Quon Kuttner (circle one) Calculators, rulers and one sheet of notes (A4 or 8.5" * 11") permitted. Show all your work on the examination sheet. ASSUME you are to explain answers briefly unless otherwise instructed. Also assume that numeric answers require units where appropriate. Place your student card where it can be inspected by the invigilators. Question Value Mark ======== ===== ==== 1 11 2 10 3 10 4 10 5 18 6 13 7 14 8 14 ===== ===== 100 1. The following appeared in a government report on the yield (in pounds per acre) of an important crop in a certain district from 1981-1987: Boxplot: data from 0.000 to 999.000 by steps of 15.0000 81) -------------------- * * ------------I + I--- -------------------- 82) ----------------- * * * -I + I------- ----------------- 83) -------- O * * ----------I + I-------- -------- 84) ------------ ** ---------I + I--------- ------------ 85) ----------------------- * -------------------------------I + I-------- ----------------------- 86) ----------------------------------------------------- ------I + I-------- ----------------------------------------------------- 87) ------------------ * ------I + I-------- ------------------ a) (1 mark) Which year was the "best" for the farmers in terms of yield? Justify your choice BRIEFLY. b) (1 mark) Which year was the "worst"? Justify your choice BRIEFLY. c) (1 mark) Which year or years had the least variable yield? Justify your choice(s) BRIEFLY.
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d) (2 marks) Actuaries want to use a Gaussian (normal) distribution model of yield in planning a crop insurance scheme. Is this appropriate or not here? Explain BRIEFLY. e) (6 marks) Suppose MINITAB had been used to analyze the data used in the example above. Let columns C1 to C7 have the data for each year with C1 being data for 1981. Explain what each of the following MINITAB commands would produce as output information. WARNING: some may not be correct, and you should identify these. All the commands and their parameters should be explained BRIEFLY. Assume there are 18 observations in each column. i) SET C10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 END PLOT C1 C10 ii) DESCRIBE C1, C4-C7 iii) STEM_AND_LEAF C4 iv) PLOT HISTOGRAM C5 2. a) (4 marks) Suppose the crop data in Q1 for 1981 has population mean 695 pounds per acre and standard deviation 275 pounds per acre. What is the probability the mean yield for 28 similar producers, chosen at random, will fall below 600 pounds per acre? Make sure you state any assumptions and explain your work. b) Give the probability distribution (along with its parameters) which describes the specified random variable in the following situations. Explain BRIEFLY. i) (2 marks) A manufacturer knows that the sugar content of the syrup in her
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91ffx - ADM 2303 Final Examination Professors Nash, Quon,...

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