A company has been receiving complaints about the attitude of some sales clerks.Over a 10-day period, the total number of complaints was 360.The company wishes to develop a control chart for the number of complaints.What would the upper control limit on the number of complaints per day be for a 3 sigma (99.7%)control chart?
A)18
B)36
C)42
D)54

Question

Quizplus · Accepted Answer

The upper control limit (UCL) for a control chart can be calculated using the formula UCL = $\bar{X} + Z\sigma$, where $\bar{X}$ is the average number of complaints per day, $Z$ is the Z-score corresponding to the desired confidence level (for 99.7% confidence, $Z = 3$), and $\sigma$ is the standard deviation. Given 360 complaints over 10 days, the average $\bar{X} = 360/10 = 36$ complaints per day. Without information on the standard deviation, we assume a Poisson distribution (common for count data), where $\sigma = \sqrt{\bar{X}} = \sqrt{36} = 6$. Thus, UCL = 36 + 3(6) = 36 + 18 = 54.

A Company Has Been Receiving Complaints About the Attitude of Some