Please answer the following question and show how you got that answer. I really appreciate it, thank you!

A customer service centre wants to develop control charts for its service waiting time. The following table shows waiting time (in minutes) for four samples for five customers for customer service call centre.

Table 1 Customer waiting times (in minutes)

Samples #1 #2 #3 #4 #5

1 4.5 4.2 4.2 4.3 4.3

2 4.6 4.5 4.4 4.7 4.3

3 4.5 4.6 4.4 4.4 4.6

4 4.7 4.6 4.8 4.5 4.9

a) Use the data in Table 1 to calculate the averages, x, and the ranges, R, of these measurements for each sample. Next, calculate the overall average, x double bar, and the average range

b) Set up three-sigma control limits for average and range. Plot the appropriate data on the control charts and determine whether the process distribution appears to be in control?

c) One more sample results in the following customer waiting times: 4.6, 4.7, 4.9, 4.8, 4.9. Use the control limits determined in part (b) to decide if the process distribution is in control.

d) Suppose that the standard deviation of the waiting time process distribution is 0.1 minutes. If customer service wants to answer all calls within 4.5 0.4 minutes, what are the upper and lower specification limits? The process is known to operate at a mean of 4.5 minutes. What are the Cp and Cpk for this process? About what percentage of all units of the product will meet specifications? If each nonconforming customer service costs the customer service centre $5, and the annual service volume is 500,000 customers, what is the annual total cost of nonconforming customer services? Is the process capable of delivering a six-sigma service quality? If not, what should the standard deviation of the process be to meet sigma six quality?