Problem #1 (this is problem #2 in Chapter 6 in the Evans text book) Auditors at the Numeros Verdes Partners took a sample of 200 accounts payable bills as shown in the Excel file: Evan-6-02-Numeros-Verdes.xlsx (click here to download the file). [a] Find the proportion 01 the bills in the sample that were paid on time? What is proportion of the bills that were overdue? Hint:you can use the countif or pivot table in Excel. (b) If an auditors takes a random sample of only 10 accounts from this population, assuming that they follow a binomial distribution what is the probability that i. Exactly 5 bills will be overdue? ii. 4 or fewer bills will be overdue? iii. 6 or more bills will be overdue? Briey explain how you solved the above problems (did you use Excel? JMP? Calculated on paper? Which formula or functions did you use, etc.) (him: for part {b} use the probabiligr, ,0, that you found in in part (a)) Problem #2 (this is problem #4 in Chapter 6 in the Evans text book) Southernwestern Punch was made by Frutayuda, Inc. and sold in 12ounce cans to benefit victims of Hurricane Zero. The mean number of ounces placed in a can by an automatic fill pump is 11.7 with a standard deviation 010.18 ounce. Assuming a normal distribution, determine the probability that the filling pump will cause an overow in a can, that is, what is the probability that more than 12 ounces will be released by the pump and overflow the can? Briey explain how you solved this problem. Problem #3 (this is problem #5 in Chapter 6 in the Evans text book] Los Alamos Green Tea is sold in 500 milliliter bottles. The standard deviation for the filling process is 7 milliliters. Assuming a normal distribution, what must the target mean for the process be to ensure that the probability of overlling more than 500 ml in a bottle is at most 1%? Briey explain how you solved this problem. Problem #4 (this is problem #5 in Chapter 1? in the Juran text book) A company has a filling machine for low pressure oxygen shells. Data collected over the past two months show an average weight after lling of 1.433g with a standard deviation 010.033g. The specication tor weight is 1.460 t 0.085g. Weight is normally distributed. [a] What percentage will not meet the weight specication? Briey explain your answer [b] Would you suggest a shift in the aim ot the filling machine? Why or why not? Problem #5 A dry cereal manufacturer has a machine for filling boxes that subsequently are sold by weight. The machine is reset depending on the type of cereal (ake, pulled), but boxes are all filled with a weight specication of 16 ounces 1 0.05 ounces. Data were collected across several runs of the two types of cereal and was saved in the file Dry-CerealJMP. Click here to download the tile. construct visuals that provide insight about the 2 filling processes and then answer the following 3 questions. Write short comments that explain your conclusions and how you solved each of the questions. [a] Compare the means and standard deviations ot the weights of the two cereals. [b] The weights of both cereals are normally distributed. What percentage of each type will not meet the weight specication? [c] Would you recommend any changes to the lling process? If so, what do you recommend