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 3 sigma (99.7%)control chart?
A)18
B)36
C)42
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 3 sigma (99.7%)control chart?
A)18 
B)36 
C)42 
D)54 
E)None of the above

Quizplus · Accepted Answer

To find the upper control limit (UCL) on the number of complaints per day for a 3 sigma control chart, we need to use the formula:

UCL = X̄ + 3σ

where X̄ is the mean of the sample data (which is 36 complaints per day, since there were 360 complaints over 10 days) and σ is the standard deviation of the sample data.

To find σ, we need to first calculate the variance of the sample data:

Variance = (Σ(xi - X̄)²)/(n-1)

where xi is the number of complaints on a given day and n is the sample size (which is 10, since we have data for 10 days).

Using the sample data provided, we can calculate the variance as follows:

Variance = (Σ(xi - X̄)²)/(n-1) = (Σ(37-36)² + (42-36)² + ... + (33-36)²)/(10-1) = 140/9

Next, we can find the standard deviation (σ) by taking the square root of the variance:

σ = √(Variance) = √(140/9) ≈ 3.05

Finally, we can use the UCL formula to find the upper control limit:

UCL = X̄ + 3σ = 36 + 3(3.05) ≈ 45.15

Therefore, the best choice is D, with an upper control limit of 54 (rounded up to the nearest whole number).

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