$15-14$ For the past two months, Suzan Shader has been concerned about machine number $5$ at the West Factory. To make sure that the machine is operating correctly, samples are taken, and the average and range for each sample are is computed. Each sample consists of $12$ items produced from the machine. Recently, $12$ samples were taken, and for each, the sample range and average were computed. The sample range and sample average were $1\mathrm{.}1$ and $46$ for the first sample, $1\mathrm{.}31$ and $45$ for the second sample, $0\mathrm{.}91$ and $46$ for the third sample, and $1\mathrm{.}1$ and $47$ for the fourth sample. After the fourth sample, the sample averages increased. For the fifth sample, the range was $1\mathrm{.}21,$ and the average was $48$; for sample number $6,$ it was $0\mathrm{.}82$ and $47$; for sample number $7,$ it was $0\mathrm{.}86$ and $50$; and for the eighth sample, it was $1\mathrm{.}11$ and $49.$ After the eighth sample, the sample average continued to increase, never getting below $50.$ For sample number $9,$ the range and average were $1\mathrm{.}12$ and $51$; for sample number $10,$ they were $0\mathrm{.}99$ and $52$; for sample number $11,$ they were $0\mathrm{.}86$ and $50$; and for sample number $12,$ they were $1\mathrm{.}2$ and $52.$ Although Suzan$$s boss wasn$$t overly concerned about the process, Suzan was. During installation, the supplier set a value of $47$ for the process average, with an average range of $1\mathrm{.}0.$ It was Suzan$$s feeling that something was definitely wrong with machine number $5.$ Do you agree? BE SURE TO PROVIDE $1)$ UPPER AND LOWER CONTROL LIMITS AND APPROPRIATE CHARTS FOR EACH PROBLEM, $2)$ MAKE A COMMENT ON WHETHER THE PROCESS IS IN OR OUT OF CONTROL $3)$ IF THE PROCESS IS "OUT OF CONTROL", WRITE A PARAGRAPH DISCUSSING WHAT ACTIONS SHOULD$/$COULD BE DONE TO CORRECT THE PROBLEM IN THE CONTEXT OF THE STORY $($may have to speculate$).$