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 $\bar { X }$ -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

Quizplus · Accepted Answer

To find the UCL, we need to use the formula:
UCL = X̄ + zσ/√n
where X̄ = 3 (average time to service a customer complaint), σ = 0.50 (standard deviation), n = 10 (sample size), and z = 3 (because we want 3 sigma limits).

Substituting the values, we get:
UCL = 3 + 3(0.50)/√10
UCL ≈ 3.43

Therefore, the UCL for the chart would be greater than 3.40 but less than or equal to 3.50, which is option C.

Historically,the Average Time to Service a Customer Complaint Has Been Xˉ\bar { X }Xˉ

Historically,the Average Time to Service a Customer Complaint Has Been $\bar { X }$