Your company's manufacturing process runs 24 hours a day. For convenience, the daily schedule is separated into 3 shifts. Day shift runs from 6am to 2pm, Evening shift 2pm - 10pm, and Night: 10pm - 6am. In addition to the hourly testing, each month the quality control department tests 420 scarves for defects. From this collection the 105 scarves are randomly selected from the Day shift, 42 scarves are selected from the Evening shift, and 273 scarves are selected from the Night shift. Last month they found that 11% of the Dayshift, 17% of the Evening, and 28% of the Night Shift scarves were defective. Question 3.4a: What is the probability that a scarf tested in the monthly collection will be from the Evening shift and working properly? Question 3.4b: What is the probability that a randomly selected scarf will be defective? Question 3.4c: What is the probability that a defective scarf was produced during the Day shift? You realize that producing such a high percentage of defective scarves may be affecting your monthly profits. Looking into the problem reveals that is a machine is producing a defect, then the defect is cause by 41% machine electronics failure 3% undertrained employees 22% an overheating processor 34% major, unrepairable, machine malfunction The cost to repair anything internal to the machine is 4198 thousand dollars, training of factory employees (which constitute 60% of all employees) costs 839.6 dollars per person, and replacing the entire machine costs $41980 Question 3.5: What is the expected repair cost of a machine that produces defective scarves? Your company's manufacturing process runs 24 hours a day. For convenience, the daily schedule is separated into 3 shifts. Day shift runs from 6am to 2pm, Evening shift 2pm - 10pm, and Night: 10pm - 6am. In addition to the hourly testing, each month the quality control department tests 420 scarves for defects. From this collection the 105 scarves are randomly selected from the Day shift, 42 scarves are selected from the Evening shift, and 273 scarves are selected from the Night shift. Last month they found that 11% of the Dayshift, 17% of the Evening, and 28% of the Night Shift scarves were defective. Question 3.4a: What is the probability that a scarf tested in the monthly collection will be from the Evening shift and working properly? Question 3.4b: What is the probability that a randomly selected scarf will be defective? Question 3.4c: What is the probability that a defective scarf was produced during the Day shift? You realize that producing such a high percentage of defective scarves may be affecting your monthly profits. Looking into the problem reveals that is a machine is producing a defect, then the defect is cause by 41% machine electronics failure 3% undertrained employees 22% an overheating processor 34% major, unrepairable, machine malfunction The cost to repair anything internal to the machine is 4198 thousand dollars, training of factory employees (which constitute 60% of all employees) costs 839.6 dollars per person, and replacing the entire machine costs $41980 Question 3.5: What is the expected repair cost of a machine that produces defective scarves
