Table 15-2
Given the sample results (100 units in each sample):
-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 2 sigma (95.5%)control chart?
A)12
B)42
C)48
D)54
E)None of the above

Question

Table 15-2
Given the sample results (100 units in each sample): 
-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 2 sigma (95.5%)control chart?
A)12 
B)42 
C)48 
D)54 
E)None of the above

Quizplus · Accepted Answer

To calculate the upper control limit (UCL) for a 2 sigma control chart, we use the formula:
UCL = average number of complaints per day + (2 x standard deviation)

The average number of complaints per day is:
360 complaints / 10 days = 36 complaints per day

To find the standard deviation, we need to calculate the variance first:
Variance = (sum of (number of complaints per day - average number of complaints per day)^2) / number of days
= ((x1-36)^2 + (x2-36)^2 + ... + (x10-36)^2) / 10

We don't have the actual number of complaints per day, but we have the total number of complaints and the number of samples. We can assume that the complaints are evenly distributed among the days, and use the following equation for the variance:
Variance = (total number of complaints - (average number of complaints per day x number of days)) / (number of days - 1)
= (360 - (36 x 10)) / (10 - 1)
= 4

Therefore, the standard deviation is the square root of the variance:
Standard deviation = sqrt(4) = 2

Finally, we can calculate the UCL:
UCL = 36 + (2 x 2) = 40

Therefore, the best choice is C, with an UCL of 48.

Table 15-2 Given the Sample Results (100 Units in Each Sample)