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A.​ Choudhury's bowling ball factory in Illinois makesbowling balls of adult size and weight only. The standard deviationin the weight of a bowling ball produced at the factory is known tobe 0.39 pounds. Each day for 24​ days, theaverage​ weight, in​ pounds, of 9 of the bowling ballsproduced that day has been assessed as​ follows:
Day
Average​ (lb.)
Day
Average​ (lb.)
Day
Average​ (lb.)
Day
Average​ (lb.)
1
16.1
7
15.9
13
16.1
19
16.1
2
16.0
8
16.0
14
16.0
20
16.1
3
16.1
9
16.0
15
16.1
21
16.0
4
16.0
10
15.9
16
16.0
22
16.0
5
15.9
11
16.1
17
16.0
23
16.1
6
16.0
12
16.0
18
15.9
24
​a) Establish a control chart for monitoring the average weightsof the bowling balls in which the upper and lower control limitsare each two standard deviations from the mean. What are the valuesof the control​ limits?
UCL=
LCL=
b) Three standard deviations from the mean
UCL=
LCL=
c) Is it in control or out of control?