Problem 1. (25 p.) A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two kilograms. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below. Weight (kilograms) Day Package 1 Package 2 Package 3 Package 4 Monday 23 22 13 24 Tuesday 23 21 19 21 Wednesday 20 19 20 21 Thursday 18 19 20 19 Friday 18 20 22 20 a. (10 p.) Develop limits for an appropriate control chart for the means of the process. b. (10 p.) Develop limits for an appropriate control chart for the ranges of the process. c. (5 p.) Is the process in control? Justify your answer. Problem 2. (25 p.) McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1 cm thick steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20 cm by 100 cm. Based on the following data, Sheet 1 2 3 4 5 6 7 8 9 10 Number of flaws 1 1 2 0 1 5 0 2 0 2 a. (15 p.) Develop limits for an appropriate control chart. b. (5 p.) Plot the control chart. c. (5 p.) Determine whether the process is in control. Justify your answer. Do you have any recommendations for the management? If so, please explain