## Calculate the lower and upper control limits, Basic Statistics

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Question:

Data entry clerks at ARCO key in thousands of insurance records each day.  They have just completed a new training program and want to establish a control chart based on the results of this training.  Each day random samples of the work of the clerks were collected.  The results are shown in the table below.  Two hundred records were sampled daily and examined for errors.  The number of records with errors was counted.

 Day Number of Records with Errors Day Number of Records with Errors 1 12 11 12 2 8 12 10 3 4 13 8 4 6 14 10 5 8 15 10 6 8 16 8 7 6 17 10 8 6 18 11 9 2 19 9 10 4 20 8

a) You want to set control limits for the proportion of records with errors.  Assume that the past twenty days performance is adequate for establishing the control limits and performing the analysis.  Using 95% control limits, what are the upper and lower control limits for the proportion of records with errors?  Calculate your proportion defective and the lower and upper control limits to 3 decimal places (0.xxx).

b) Plot the control chart and the sample values.

c)  What would you conclude about the process, in other words, is the process in control?  Explain your decision.

d)  Suppose the industry's lower and upper control limits are 0.020 and 0.050 respectively.  What can this insurance company conclude about its process relative to the industry standards?

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