In: Statistics and Probability
Day |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Number of Aides Absent |
5 |
8 |
11 |
15 |
4 |
2 |
7 |
1 |
4 |
6 |
14 |
19 |
3 |
5 |
8 |
Solution:
Pbar can be calculated as
Pbar = Total no. of absenteeism/Total no. of sample =
(5+8+11+15+15+4+2+7+1+4+6+14+19+3+5+8)/1500 = 112/1500 =
0.0747
UCL ca be calculated as
Pbar + 3*sqrt(Pbar*(1-pbar)/n) = 0.0747 +
3*sqrt(0.0747*(1-0.0747)/100) = 0.1536
So its answer is B. i.e. 0.1536
LCL can be calculated as
Pbar - 3*sqrt(Pbar*(1-pbar)/n) = 0.0747 -
3*sqrt(0.0747*(1-0.0747)/100) = 0
So its answer is A. i.e. o to 0.0030
Day |
No. Of Absent |
Proportion Of Absentism (No. Of Absent/100) |
1 |
5 |
0.05 |
2 |
8 |
0.08 |
3 |
11 |
0.11 |
4 |
15 |
0.15 |
5 |
4 |
0.04 |
6 |
2 |
0.02 |
7 |
7 |
0.07 |
8 |
1 |
0.01 |
9 |
4 |
0.04 |
10 |
6 |
0.06 |
11 |
14 |
0.14 |
12 |
19 |
0.19 |
13 |
3 |
0.03 |
14 |
5 |
0.05 |
15 |
8 |
0.08 |
From the Proportion we can say that all absent proportion are
between 0 to 0.1536 except day12.
so we can say that absenteeism is our of statistical control
because you found one day out of the control limits.
So its answer is B.