Question

A professor records the number of students who complain each week throughout the semester. If the class size is forty students, what are 3-sigma control limits for this class? Construct a control chart and interpret the data. ( p chart).

Week #	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Complaints	5	2	7	1	3	2	8	1	3	5	4	6	3	1	4

Answer 1

Z = 3
SAMPLES = 40
SAMPLE TIME = 15

P = NO. OF DEFECTS / (SAMPLE * TIMES TAKEN) = 55 / (40 * 15) = 0.0917
STANDARD DEVIATION = SQRT((P * (1 - P)) / SAMPLES = SQRT((0.0917 * (1 - 0.0917)) / 40 = 0.0456

UCL = P + (Z * STANDARD DEVIATION) = 0.0917 + (3 * 0.0456) = 0.2285
LCL = P - (Z * STANDARD DEVIATION) = 0.0917 - (3 * 0.0456) = -0.0451, LCL < 0, THEREFORE, LCL = 0

BASED ON THE CONTROL CHART, ALL THE OBSERVATIONS ARE UNDER CONTROL

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