Question: Tony Perez is the manager of one of the largest chains of service stores that specialize in oil and lubrication of automobiles, Fastlube, Inc. One of the company's stated goals is to provide a lube and oil change for anyone's automobile in 15 minutes. Tony has thought for some time now that there is a growing disparity among his workers in the time it takes to lube and change the oil of an automobile. To monitor this aspect of Fastlube, Tony has selected a sample of 20 days and has recorded the time it took five randomly selected employees to service an automobile. The data are located in the file Fastlube.
a. Tony glanced through the data and noticed that the longest time it took to service a car was 25.33 minutes. Suppose the distribution of times to service a car was normal, with a mean of 15. Use your knowledge of a normal distribution to let Tony know what the standard deviation is for the time it takes to service a car.
b. Use the Fastlube data to construct an x and an R-chart.
c. Based on these data, what would you conclude about the service process?
d. Based on your findings on the R-chart, would it be advisable to draw conclusions based on the x-chart?