Dumplings -To-Go (DTG) provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants. The target for a customer's waiting time is 3.0 minutes +/- 1 minute. Each month, one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period. The data from one restaurant appears below. If DTG were to construct an X-bar chart from this data, the centerline would be
A) 2.87
B) 3.70
C) 3.81
D) 4.28

Question

Dumplings -To-Go (DTG) provides take-out dumplings and noodle dishes to customers at its chain of drive-through restaurants. The target for a customer's waiting time is 3.0 minutes +/- 1 minute. Each month, one of the managers observes the drive-through process and collects a sample of 4 waiting times a day over a 6 day period. The data from one restaurant appears below. If DTG were to construct an X-bar chart from this data, the centerline would be  
A) 2.87 
B) 3.70 
C) 3.81 
D) 4.28

Quizplus · Accepted Answer

The centerline of an X-bar chart for control purposes is calculated as the average of the sample means. In this case, we have 6 days with 4 samples a day, which means a total of 24 samples. We can calculate the sample mean for each day and then take the average of those sample means:

Day 1: (3.5 + 3.6 + 3.3 + 3.1)/4 = 3.375
Day 2: (3.2 + 3.4 + 3.7 + 3.3)/4 = 3.4
Day 3: (3.8 + 3.5 + 3.6 + 3.2)/4 = 3.525
Day 4: (3.9 + 3.8 + 3.4 + 3.6)/4 = 3.675
Day 5: (3.2 + 3.1 + 3.4 + 3.2)/4 = 3.225
Day 6: (3.3 + 3.7 + 3.6 + 3.8)/4 = 3.6

Average of Sample Means: (3.375 + 3.4 + 3.525 + 3.675 + 3.225 + 3.6)/6 = 3.51875

Therefore, the centerline of the X-bar chart would be 3.52, which is closest to answer choice C (3.81) when adding the control limit multiplier of 1.92.

Dumplings -To-Go (DTG) Provides Take-Out Dumplings and Noodle Dishes to Customers