A hotel tracks the number of complaints per month. When the process is in control, there is an average of 35 complaints per month. Assume that a 2-sigma control limit is used. What is the upper control limit?
A) less than or equal to 35
B) more than 35 but less than or equal to 45
C) more than 45 but less than or equal to 55
D) more than 55

Question

Quizplus · Accepted Answer

A 2-sigma control limit means that the upper control limit is 2 standard deviations above the mean. Assuming a normal distribution, this would place the upper control limit at 35 + (2*sigma), where sigma is the standard deviation of the complaints. Without knowledge of the standard deviation, we cannot compute the exact upper control limit. However, we can use the empirical rule, which states that about 95% of the data lies within 2 standard deviations of the mean. Since we are assuming that the process is in control, we can assume that the standard deviation is relatively small. Therefore, we can estimate the upper control limit to be somewhere around 45 (35 + (2*5)). This falls within option C) more than 45 but less than or equal to 55.

A Hotel Tracks the Number of Complaints Per Month