\"Please solve this problem, including building the X-bar charts, using MS Excel
ID: 376919 • Letter: #
Question
"Please solve this problem, including building the X-bar charts, using MS Excel. I recommend creating a separate spreadsheet tab for part (a) and for part (b), z=2 and z=3 respectively. Answer the "Why" of part (b) in the spreadsheet at the top of the page. See the sample problem (S6.6 modified for X-bar chart, as we did in the lab) for guidance on how to set this problem up."
Kime's bowling ball factory makes bowling balls of only. The standard deviation in the weight of a roduced at the factory is known to be 0.12 pounds. Each s, the average weight, in pounds, of nine of the bowling bowling .. s6.8 Bill adult size and weight bowling ball day for 24 days, s weigh produced that day has been assessed as follows: Average (lb) 16.3 15.9 15.8 15.5 16.3 16.2 16.0 16.1 15.9 16.2 15.9 15.9 Day 13 Average (lb) 16.3 15.9 16.3 16.2 16.1 15.9 16.2 15.9 15.9 16.0 15.5 15.8 Day 15 4 17 19 20 21 10 23 24 12 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? three standard deviations are used in the chart, how do these val ues change? Why? Px Whole Grains LLC uses statistical process control t have at is ealth-conscious, low-fat, multigrain sandwich loaves that its health-co ualu ctahle and in-controExplanation / Answer
day
average (lb)
std dev
0.12
lb
1
16.3
UCL=x bar+ z * std dev
2
15.9
LCL = x bar - z* std dev
3
15.8
4
15.5
a) z
2
5
16.3
UCL
16.24
6
16.2
LCL
15.76
7
16.0
8
16.1
b)z
3
9
15.9
UCL
16.36
10
16.2
LCL
15.64
11
15.9
12
15.9
if 3 std deviations are used in the chart, the UCL and LCL values shift further away from the mean (x bar) in the chart.
13
16.3
As we move from 2 std deviations from the mean to 3 std deviations from the mean, the acceptable value zone in the chart will expand, as now values till 3 std deviations from the mean are allowed on both side of the mean instead of 2.
14
15.9
as with 2 std deviation away from mean, 97.73% area around the mean was acceptable, while when we take 3 std deviations from the mean, 99.87% of area around the mean was acceptable
15
16.3
16
16.2
17
16.1
18
15.9
19
16.2
20
15.9
21
15.9
22
16.0
23
15.5
24
15.8
x bar
16.0
day
average (lb)
std dev
0.12
lb
1
16.3
UCL=x bar+ z * std dev
2
15.9
LCL = x bar - z* std dev
3
15.8
4
15.5
a) z
2
5
16.3
UCL
16.24
6
16.2
LCL
15.76
7
16.0
8
16.1
b)z
3
9
15.9
UCL
16.36
10
16.2
LCL
15.64
11
15.9
12
15.9
if 3 std deviations are used in the chart, the UCL and LCL values shift further away from the mean (x bar) in the chart.
13
16.3
As we move from 2 std deviations from the mean to 3 std deviations from the mean, the acceptable value zone in the chart will expand, as now values till 3 std deviations from the mean are allowed on both side of the mean instead of 2.
14
15.9
as with 2 std deviation away from mean, 97.73% area around the mean was acceptable, while when we take 3 std deviations from the mean, 99.87% of area around the mean was acceptable
15
16.3
16
16.2
17
16.1
18
15.9
19
16.2
20
15.9
21
15.9
22
16.0
23
15.5
24
15.8
x bar
16.0
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