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 $ \bar{x} $ 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 for the chart, we need to use the formula:

UCL = ̅X + 3σ/√n

where ̅X is the average time to service a customer complaint (3 days), σ is the standard deviation (0.50 day) and n is the sample size (10).

UCL = 3 + 3(0.50)/√10 ≈ 3.49

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

Historically, the Average Time to Service a Customer Complaint Has xˉ \bar{x} xˉ

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