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ismch16 - 72 Instructors Solutions Manual for Statistics...

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72 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition Chapter 16: Introduction to Quality 16-1 thru 5. Various answers. 16.6 a. 4 ˆ / 5.42/.959 5.6517 s c σ = = = b. CL = X = 192.6 LCL = 3 3 4 3 , X A s where A c n - = = 192.6 – 1.18(5.42) = 186.2044 UCL = 3 3 4 3 , X A s where A c n + = = 192.6 + 1.18(5.42) = 198.9956 c. CL = 5.42 LCL = .12(5.42) = .6504 UCL = 1.88(5.42) = 10.1896 16.7 a. ˆ 3.67 /.952 3.855 σ = = b. CL = 93.2 LCL = 93.2 – 1.29(3.67) = 88.4657 UCL = 93.2 + 1.29(3.67) = 97.9343 c. CL = 3.67 LCL = .03(3.67) = .1101 UCL = 1.97(3.67) = 7.2299 16.8 a. ˆ 1.23/.965 1.2746 σ = = b. CL = 19.86 LCL = 19.86 – 1.1(1.23) = 18.507 UCL = 19.86 + 1.1(1.23) = 21.213 c. CL = 1.23 LCL = .18(1.23) = .2214 UCL = 1.82(1.23) = 2.2386 16.9 a. ˆ 1.75/.940 1.8617 σ = = b. CL = 230.5 LCL = 230.5 – 1.43(1.8617) = 227.8378 UCL = 230.5 + 1.43(1.8617) = 233.1622 c. CL = 1.75 LCL = 0(1.75) = 0.0 UCL = 2.09(1.75) = 3.6575 16.10 a. 4999.4/30 149.98 x = = b. 179.67 / 30 5.989 s = = c. ˆ 5.989/.965 σ = = 6.2062 d. CL = 149.98 LCL = 149.98 – 1.1(5.989) = 143.3921 UCL = 149.98 + 1.1(5.989) = 156.5679
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73 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition e. The X chart shows a process where the level is under statistical control 30 20 10 0 160 150 140 Sample Number Sample Mean X-bar Chart for Exercise 16-10 Mean=149.98 UCL=156.57 LCL=143.39 f. CL = 5.989 LCL = .18(5.989) = 1.078 UCL = 1.82(5.989) = 10.9 g. S-chart 10 20 30 0 2 4 6 8 10 12 Index Sample StDev S Chart for 16-10 S BAR=5.989 LCL=1.078 UCL=10.9
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Chapter 16: Introduction to Quality 74 16-11 a. 396.8/ 20 19.84 x = = b. 39.8/ 20 1.99 s = = c. ˆ 1.99/.952 σ = = 2.0903 d. CL = 19.84 LCL = 19.84 – 1.29(1.99) = 17.2729 UCL = 19.84 + 1.29(1.99) = 22.4071 e. 20 10 0 22 21 20 19 18 Sample Number Sample Mean X-bar Chart for XBar_16- Mean=19.84 UCL=21.90 LCL=17.78 f. CL = 1.99, LCL = .03(199) = .0597, UCL = 1.97(1.99) = 3.9203 g. S Chart
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75 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 20 15 10 5 4 3 2 1 0 Index Sample StDev S Chart for 16-11 UCL=3.9203 S BAR=1.99 LCL=.0597 16.12 a. 192.6 ± 3(5.6517): (175.6449, 209.5551) These values lie within the tolerance limits b. 215 170 1.327 6(5.6517) p C - = = The process is not capable since 1.33 p C < c. 215 192.6 1.321 3(5.6517) pk C - = = The process is not capable since 1.33 pk C < 16.13 a. 93.2 ± 3(3.855): (81.635, 104.765) These limits are beyond the tolerances set by management b. 100 85 .648 6(3.855) p C - = = The process is not capable since 1.33 p C < c. 100 93.2 .588 3(3.855) pk C - = = The process is not capable since 1.33 pk C < 16.14 a. 19.86 ± 3(1.2746): (16.0362, 23.6838) These limits are beyond the tolerances set by management b. 22 18 .523 6(1.2746) p C - = = The process is not capable since 1.33 p C < c. 19.86 18 .486 3(1.2746) pk C - = = The process is not capable since 1.33 pk C < 16.15 a. 149.98 ± 3(6.2062): (131.3614, 168.5986)
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Chapter 16: Introduction to Quality 76 These values lie within the tolerance limits b. 170 130 1.074 6(6.2062) p C - = = The process is not capable since 1.33 p C < c. 149.98 130 1.073 3(6.2062) pk C - = = The process is not capable since 1.33 pk C < 16.16 a. 19.84 ± 3(2.0903): (13.5691, 26.1109) These limits are beyond the tolerances set by management b. 24 16 .638 6(2.0903) p C - = = The process is not capable since 1.33 p C < c. 19.84 16 .612 3(2.0903) pk C - = = The process is not capable since 1.33 pk C < 16.17 CL = .056, LCL = .056 – 3 .056(.944) 250 = .0124 UCL = .056 + 3 .056(.944) 250 = .0996 16.18 CL = .016, LCL = 0, UCL = .016 + 3 .016(.984) 500 = .0328 16.19 a. 3.74/30 .1247 p = = , CL = .1247, LCL = .1247 – 3 .1247(.8753) / 200 = .0546
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77 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition UCL= .1247 + 3 .1247(.8753) / 200 = .1948 b. p-chart 30 20 10 0 0.20 0.15 0.10 0.05 Sample Number Proportion P Chart for Exercise 16-19 P=0.1247 UCL=0.1947 LCL=0.05459 The p-chart shows a process that is in statistical control
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Chapter 16: Introduction to Quality 78 16.20 a. 1.02/ 20 .051 p = = , CL = .051, LCL = .051 – 3 .051(.949) /500 = .0215 UCL = .051 + 3 .051(.949) /500 = .0805 b. p-chart 20 10 0 0.085 0.075 0.065 0.055 0.045 0.035 0.025 0.015 Sample Number Proportion P Chart for Exercise 16-20 P=0.051 UCL=0.08052 LCL=0.02148 No evidence that the process is out of statistical control
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79 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 16.21 a.
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