The time to make beds at a motel is supposed to fall into an agreed-on range of times. A sample of five maids was selected to evaluate their efficiency, and the time needed to make a bed was observed on three different occasions:

Service Time (in seconds)

_____Maid Sample 1 Sample 2 Sample 3_____

Holland 110 90 150

Lindsey 180 120 140

Marie 155 130 175

Cindy 120 140 90

Manny 140 185 155

______________________________________________________________________________

1.

What are the upper and lower control limits for an X-bar chart with a sample size of five?

	a.	UCL = 186.76, LCL = 90.64
	b.	UCL = 191.87, LCL = 85.47
	c.	UCL = 196.06, LCL = 96.44
	d.	UCL = 168.67, LCL = 108.67
	e.	None of the above

2.

What are the upper and lower control limits for an R chart with a sample size of five?

	a.	UCL = 109.93, LCL = 0
	b.	UCL = 133.85, LCL = 0
	c.	UCL = 155.93, LCL = 0
	d.	UCL = 176.16, LCL = 0
	e.	None of the above

3.

After the control chart was established, a sample of five observations had the following time in seconds: 182, 150, 192, 178, 100. Is corrective action called for?

	a.	X-bar = 160.2; process is out of control, corrective action is needed
	b.	X-bar = 160.2.2, R-bar = 111; process is in control, no corrective action is needed
	c.	X-bar = 160.2, R-bar = 111; process is out of control, corrective action is needed
	d.	X-bar = 176.25, R-bar = 42; process is in control, no corrective action is needed
	e.	None of the above

4.

An operator of a mechanized sorting machine in the post office must read the zip code on a parcel and, knowing its location in the city, divert the package to its proper truck route. Based on past records, the error rate for skilled operators is approximately five errors per 100 parcels sorted - a defective rate of .05. Management wants to develop a control chart to monitor new operators to make sure that employees who are unsuited for the job can be identified. Over a nine-day probationary period, random samples of 100 parcels are drawn from the truck routes. What are the control limits for the sorting operation?

	a.	UCL = .05, LCL = 0
	b.	UCL = .09, LCL = .01
	c.	UCL = .11, LCL = 0
	d.	UCL = .37, LCL = 0
	e.	None of the above

5.

After becoming more experienced with their jobs, the machine operators in question 4 averaged only two sorting errors per 100 parcels sorted. What are the new control limits for the sorting operation?

	a.	UCL = .02, LCL = 0
	b.	UCL = .06, LCL = 0
	c.	UCL = .35, LCL = 0
	d.	UCL = .04, LCL = .004
	e.	None of the above

6.

The following table shows samples of response times for an emergency ambulance service. The data cover a historically representative seven days. Four response calls were picked at random each day: one during the morning, afternoon, evening and night shift for each day.

Day

Shift	1	2	3	4	5	6	7
Morning	3.6	4.5	2.9	7.1	4.3	6.7	2.8
Afternoon	5.2	6.3	4.7	6.2	2.8	5.8	5.6
Evening	6.5	7.2	3.8	3.9	5.9	6.9	3.8
Night	4.9	6.9	4.3	5.6	3.2	4.9	4.9

What are the upper and lower control limits for an X-bar chart of the ambulance service with a sample size of four?

	a.	UCL = 6.1, LCL = 3.9
	b.	UCL = 6.6, LCL = 3.5
	c.	UCL = 6.9, LCL = 3.1
	d.	UCL = 7.7, LCL = 2.4
	e.	None of the above

5 points

Question 7

Using the data in question 6, what are the upper and lower control limits for an R chart with a sample size of four?

	a.	UCL = 5.9, LCL = 0
	b.	UCL = 7.02, LCL = 0
	c.	UCL = 7.02, LCL = 0.28
	d.	UCL = 8.3, LCL = 0
	e.	None of the above

7.

After the emergency ambulance service in question 6 had established its control chart, the following week, on the fifth day of Spring Break, the following sample of ambulance response times (in minutes) was collected: 4.8, 6.5, 7.9, 8.5. Based on these data, should the ambulance service be concerned about its performance?

	a.	No, X-bar = 6.9, R-bar = 3.7; sample mean and range are in control limits; no corrective action is needed.
	b.	Yes, X-bar = 6.9, R-bar = 3.7; sample mean and range are outside control limits; corrective action is needed.
	c.	Yes, X-bar = 6.9, R-bar = 3.7; sample mean is within control limit, sample range is outside control limit; corrective action is needed.
	d.	Yes, X-bar = 6.9, R-bar = 3.7; sample mean is on control limit and last two response times are outside of control limits; corrective action should be taken.
	e.	None of the above.