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.Suppose the next sample of 10 yielded the following result: 3.2,2.1,3.6,2.8,3.9,3.5,2.7,4.1,2.6,and 3.3.What conclusion can be drawn?
A)Assuming the process variability is in control,the process average is also in statistical control.
B)Assuming the process average is in control,the process average is out of statistical control.
C)The sample size should be increased.
D)No conclusion can be drawn because there is insufficient data.

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.Suppose the next sample of 10 yielded the following result: 3.2,2.1,3.6,2.8,3.9,3.5,2.7,4.1,2.6,and 3.3.What conclusion can be drawn?
A)Assuming the process variability is in control,the process average is also in statistical control. 
B)Assuming the process average is in control,the process average is out of statistical control. 
C)The sample size should be increased. 
D)No conclusion can be drawn because there is insufficient data.

Quizplus · Accepted Answer

To determine if the process is in control, we need to calculate the control limits. We are given that the historical average is 3 days and the standard deviation is 0.50 day. Using this information, we can calculate the control limits for an 11eab530_ae79_b252_9198_09b5ef244f7f_TB2904_11 chart with a sample size of 10 and 3-sigma limits:

Upper Control Limit (UCL) = Historical Average + (3 x Standard Deviation/√Sample Size) = 3 + (3 x 0.50/√10) = 3.48
Lower Control Limit (LCL) = Historical Average - (3 x Standard Deviation/√Sample Size) = 3 - (3 x 0.50/√10) = 2.52

The next sample of 10 observations yielded an average of 3.14, which is within the control limits (2.52 to 3.48). Therefore, assuming the process variability is in control, we can conclude that the process average is also in statistical control.

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