Question

.S6.8 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 0.12 pounds. Each day for 24 days, the average weight, in pounds, of nine of the bowling balls produced that day has been assessed as follows: AVERAGE (LB) DAY AVERAGE (LB) DAY 16.3 13 16.3 15.9 15.9 2 16.3 15 15.8 3 16.2 16 15.5 16.1 17 16.3 15.9 18 16.2 16.2 19 16.0 15.9 20 16.1 8 15.9 21 15.9 9 16.0 16.2 15.5 23 15.9 15.8 24 15.9 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? b. If three standard deviations are used in the chart, how do these values change? Why? Px

Answer 1

(a)

Day	Average lbs.	CL	LCL	UCL	Average	16
1	16.3	16	15.92	16.08	Standard deviation (σ)	0.12
2	15.9	16	15.92	16.08	Sample size (n)	9
3	15.8	16	15.92	16.08	Standard error = σ / √n	0.04
4	15.5	16	15.92	16.08
5	16.3	16	15.92	16.08	UCL	16.08
6	16.2	16	15.92	16.08	LCL	15.92
7	16.0	16	15.92	16.08
8	16.1	16	15.92	16.08
9	15.9	16	15.92	16.08
10	16.2	16	15.92	16.08
11	15.9	16	15.92	16.08
12	15.9	16	15.92	16.08
13	16.3	16	15.92	16.08
14	15.9	16	15.92	16.08
15	16.3	16	15.92	16.08
16	16.2	16	15.92	16.08
17	16.1	16	15.92	16.08
18	15.9	16	15.92	16.08
19	16.2	16	15.92	16.08
20	15.9	16	15.92	16.08
21	15.9	16	15.92	16.08
22	16.0	16	15.92	16.08
23	15.5	16	15.92	16.08
24	15.8	16	15.92	16.08

AB 2 Day Average lbs. CL 1 16.3 2 15.9 3 15.8 4 15.5 516..3 6 16.2 7 16 8 16.1 9 15.9 10 16.2 11 15.9 12 15.9 13 16.3 14 15.9 15 16.3 16 16.2 17 16.1 18 15.9 19 16.2 20 15.9 21 15.9 22 16 23 15.5 24 15.8 LCL UCL Average =AVERAGE(C3:C26) $H$2 $H$8 $H$7Standard deviation ( 0.12 SH$2SH$8 $H$7 Sample size (n) -$H$2 $H$8 $H$7 Standard error o /Vn H3/SQRT(H4) 4 Control chart 10 12 13 14 15 16 17 18 19 20 21 $H$2 $H$8$H$7 16.3 $H$2 $H$8 $H$716.2 $H$2 $H$8 $H$716.1 16.08 16 15.92 15.8 15.6 15.4 23 24 25 26 10 15 20 25 30 Average lbs.- CL_

(b)

Average	=AVERAGE(C3:C26)
Standard deviation (σ)	0.12
Sample size (n)	9
Standard error = σ / √n	=H3/SQRT(H4)
UCL	=H2+3*H5
LCL	=H2-3*H5

UCL	16.12
LCL	15.88