A major automobile company is interested in reducing the time that customers have to wait while having

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A major automobile company is interested in reducing the time that customers have to wait while having their car serviced with one of the dealers. They select four customers randomly each day and find the total time that each customer has to wait (in minutes) while his or her car is serviced. From these four observations, the sample average and range are found. This process is repeated for 25 days. The summary data for these observations are
A major automobile company is interested in reducing the time

(a) Find the - and R-chart control limits
(b) Assuming that the process is in control and the distribution of waiting time is normal, find the percentage of customers who will not have to wait more than 50 minutes.
(c) Find the 2σ control limits.
(d) The service manager is developing a promotional program and is interested in reducing the average waiting time to 30 minutes by employing more mechanics. If the plan is successful, what proportion of the customers will have to wait more than 40 minutes? More than 50 minutes?

Distribution
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