The following table shows samples of response times for an emergency ambulance s
ID: 335468 • Letter: T
Question
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?
UCL = 6.1, LCL = 3.9
UCL = 6.6, LCL = 3.5
UCL = 6.9, LCL = 3.1
UCL = 7.7, LCL = 2.4
None of the above
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
Explanation / Answer
For n=4, the value of
A2 is given as 0.729 ( from A2 table)
The formula for UCL is given as below:-
UCL Xbar=X double bar+A2(R bar)
UCL=5.045+0.729*3.725
UCL=7.76
The formula for LCL is given as below:-
LCL Xbar=X double bar-A2(R bar)
LCL=5.045-0.729*3.725
LCL=2.33
So the correct Answer is:- D:- UCL = 7.7, LCL = 2.4
Shift 1 2 3 4 5 6 7 X bar Range Morning 3.6 4.5 2.9 7.1 4.3 6.7 2.8 (3.6+4.5+2.9+7.1+4.3+6.7)/6 4.56 7.1-2.8 4.3 Afternoon 5.2 6.3 4.7 6.2 2.8 5.8 5.6 (5.2+6.3+4.7+6.2+2.8+5.8)/6 5.23 6.3-2.8 3.5 Evening 6.5 7.2 3.8 3.9 5.9 6.9 3.8 (6.5+7.2+3.8+3.9+5.9+6.9)/6 5.43 7.2-3.8 3.4 Night 4.9 6.9 4.3 5.6 3.2 4.9 4.9 (4.9+6.9+4.3+5.6+3.2+4.9)/6 4.96 6.9-3.2 3.7 Average 5.045 3.725Related Questions
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