A.? Choudhury's bowling ball factory in Illinois makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.36 pounds. Each day for 24? days, the average? weight, in? pounds, of 9 of the bowling balls produced that day has been assessed as? follows:
|
Day
|
Average? (lb.)
|
Day
|
Average? (lb.)
|
Day
|
Average? (lb.)
|
Day
|
Average? (lb.)
|
|
1
|
10.4
|
7
|
9.7
|
13
|
9.6
|
19
|
9.7
|
|
2
|
9.8
|
8
|
9.7
|
14
|
9.7
|
20
|
10.0
|
|
3
|
9.5
|
9
|
9.6
|
15
|
9.6
|
21
|
9.5
|
|
4
|
10.0
|
10
|
10.1
|
16
|
10.1
|
22
|
9.7
|
|
5
|
9.5
|
11
|
9.6
|
17
|
9.7
|
23
|
9.7
|
|
6
|
10.2
|
12
|
9.9
|
18
|
9.7
|
24
|
9.8
|
a) Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean. What are the values of the control? limits?
Upper Control Limit ?(UCLx?)=________ Lb. ? (round your response to two decimal? places).
Lower Control Limit ?(LCLx?)=________ Lb.? (round your response to two decimal? places).
?b) If three standard deviations are used in the? chart, what are the values of the control? limits?
Upper Control Limit ?(UCLx?)=_________lb. ? (round your response to two decimal? places).
Lower Control Limit ?(LCLx?)=_________lb. ?(round your response to two decimal? places).
How do these values change?
a) The control limits are tighter for the ?2-sigma x ?-chart than for the ?3-sigma x?-chart.
b) The control limits for the 2?-sigma x ?-chart and for the ?3-sigma x?-chart are the same.
c) The control limits are tighter for the ?3-sigma x?-chart than for the ?2-sigma x?-chart.