Needing help understanding and figuring out this question... the solutions on Ch
ID: 420930 • Letter: N
Question
Needing help understanding and figuring out this question... the solutions on Chegg didn't provide any formulas. Trying to identify the upper and lower control limits.
An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of 1.00 liter and a standard deviation of 0.05 liter. Output is monitored using means of samples of 26 observations. Use Table-A (At bottom).
a.Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. (Do not round intermediate calculations. Round z value to 2 decimal places. Round your answers to 4 decimal places.)
Upper control limits:
Lower control limits:
Upper control limits:
Lower control limits:
Table A Areas under the normal curve, 0 to z 07 8 0120 0517 0910 1293 1664 0319 0714 1103 1480 1844 0160 0199 0478 0871 1255 1628 0675 1026 1406 1772 1064 1808 2157 1141 1517 1879 1217 1331 1700 1736 1591 1950 2611 1915 2190 2517 1985 2019 2123 2257 2422 2673 2967 3051 3315 2881 2910 3106 3133 3159 3413 3849 4192 3212 3461 3749 3810 4015 4177 4319 4049 4147 4115 4265 4162 4251 4418 4616 4756 4441 4474 4495 4505 4554 4641 4713 4573 4726 4783 4678 4744 4649 4719 4778 4706 4767 4732 4738 4750 4761 4772 4861 4918 4793 4798 4842 4788 4812 4817 4909 4911 4906 4929 4901 4913 4916 4941 4938 4953 4965 4974 4981 4948 4961 4946 4951 4955 4966 4969 4970 4978 4984 4973 4974 4977 4979 4987 4989 4989Explanation / Answer
97% = 0.97
Use table A (as provided in the question) to find the corresponding z value. We will look for 0.97/2 = 0.4850
From the table we can see that 0.4850 is present when the z column is 2.1 and the z row is 0.07. Thus z value = 2.1+0.07 = 2.17
UCL = mean + (z*standard deviation)/square root of n = 1 + (2.17*0.05)/square root of 26 = 1+0.0213 = 1.0213
LCL = mean - (z*standard deviation)/square root of n = 1 - (2.17*0.05)/square root of 26 = 1 – 0.0213 = 0.9787
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