At a fast-food restaurant,if the average time to serve a customer is 3.75 minutes for 10 samples of size 5,and the average range for the samples is 0.50 minutes,the upper and lower control limits for a 3-sigma x-chart are
A)UCL = 4.04,LCL = 3.46
B)UCL = 5.08,LCL = 4.94
C)UCL = 5.75,LCL = 1.75
D)UCL = 3.91,LCL = 3.60

Question

Quizplus · Accepted Answer

To calculate the control limits for the x-chart:
Mean (X-Bar) = 3.75 minutes
Range (R-Bar) = 0.5 minutes

Upper Control Limit (UCL) = X-Bar + A2 * R-Bar
Lower Control Limit (LCL) = X-Bar - A2 * R-Bar

Here, for a sample size of 5, the value of A2 from the standard normal distribution table is 0.577.

Using the formula:
UCL = 3.75 + 0.577 * 0.5 = 4.04
LCL = 3.75 - 0.577 * 0.5 = 3.46

Therefore, the correct answer is (A).

At a Fast-Food Restaurant,if the Average Time to Serve a Customer