Janice Sanders, CEO of Pine Crest Medical Clinic, is concerned over the number o

Question

Janice Sanders, CEO of Pine Crest Medical Clinic, is concerned over the number of times patients must wait more than 30 minutes beyond their scheduled appointments. She asked her assistant to take random samples of 65 patients to see how many in each sample had to wait more than 30 minutes. Each instance is considered a defect in the clinic process. The table below contains the data for 15 samples Number of Number of Number of Sample DefectsSampleDefects Sample Defects 12 13 14 10 a. Assuming Janice Sanders is willing to use three-sigma control limits, construct the upper and lower control limits. The UCL, equals and the LCL squalsEnter your responses rounded to four decimal places. if your answer for LCL, is negative, enter this value as 0)

Explanation / Answer

First we will calculate mean number of defects = Number of defects/ Numberof samples

= 88/15 = 5.87

Here Eachsample size = 65 patients

so Mean proportional defects in a sample p^ = 5.87/ 65 = 0.0903

LCLp = p^ - 3 * sqrt [p^ * (1-p^)/ N] = 0.09 - 3 * sqrt [0.0903 * 0.9097/65] = -0.0165 = 0

UCLp = p^ +  3 * sqrt [p^ * (1-p^)/ N] = 0.09 + 3 * sqrt (0.09 * 0.91/65) = 0.1969

LCLp = 0

UCLp = 0.1969

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