Historically,the average time to service a customer complaint has been 3 days and the standard deviation has been 0.50 day.Management would like to specify the control limits for an chart with a sample size of 10 and 3- sigma limits.The UCL for the chart would be:
A)less than or equal to 3.30.
B)greater than 3.30 but less than or equal to 3.40.
C)greater than 3.40 but less than or equal to 3.50.
D)greater than 3.50.

Question

Historically,the average time to service a customer complaint has been 3 days and the standard deviation has been 0.50 day.Management would like to specify the control limits for an  chart with a sample size of 10 and 3- sigma limits.The UCL for the chart would be:
A)less than or equal to 3.30. 
B)greater than 3.30 but less than or equal to 3.40. 
C)greater than 3.40 but less than or equal to 3.50. 
D)greater than 3.50.

Quizplus · Accepted Answer

For a control chart with a sample size of 10 and 3-sigma limits, the formula for the upper control limit (UCL) is:
UCL = Average + 3*(Standard Deviation/Square root of sample size)
Plugging in the given values:
Average = 3 days
Standard Deviation = 0.50 day
Sample size = 10
UCL = 3 + 3*(0.50/sqrt(10)) = 3.45
Therefore, the UCL would be greater than 3.40 but less than or equal to 3.50, which corresponds to choice C.

Historically,the Average Time to Service a Customer Complaint Has Been