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Suppose that we are making an auto part and that the mean length of the part is 5 inches with standard deviation of 0.25 inches, and the length is normally distributed. The upper ecification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table provided on the next page.

Suppose that we are making an auto part and that the mean length of the part is 5 inches with standard deviation of 0.25 inches, and the length is normally distributed. The upper ecification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table provided on the next page.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Number in the table represents P(Z≤2) z 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.6 .0002 .0002 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 -3.5 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 -3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 -3.0.0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 -2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 -2.3 .0107 0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 -2.1 .0179 .0174 0170 .0166 .0162 .0158 0154 .0150 0146 .0143 -2.0.0228 .0222 .0217 .0212 .0207 .0202 0197 .0192 0188 .0183 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 -1.8 .0359 -1.7 .0446 .0436 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 .1788 .1762 .1736 2061 .2033 .2005 -1.5 .0668 .0655 .0643 .0630 .0618 .0606 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 -1.3 .0968 .0951 .0934 .0918 .0901 .0885 -1.2 1151 .1131 .1112 .1093 .1075 .1056 -1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 -0.9 .1841 .1814 .1711 .1685 .1660 -0.8 2119 .2090 .0594 .0582 .0721 .0708 .0694 .0869 .0853 .0838 .0823 .1038 .1020 .1003 .0985 .0571 .0559 .0681 .1423 .1401 .1379 .1635 .1611 .1977 .1949 .1922 .1894 .1867 -0.7 .2420 2389 2358 .2327 .2296 .2266 2236 .2206 .2177 .2148 -0.6 .2743 2709 2676 2643 .2611 -0.5 .3085 3050 -0.4 .3446 3409 -0.3 .3821 .3783 -0.2 .4207 .4168 -0.1 .4602 .4562 -0.0 .5000 .4960 3015 .2981 .2946 .3372 .3336 .3300 .3745 .3707 .3669 4129 .4090 .4052 .4522 4483 4443 .4920 .4880 .4840 2578 2546 .2912 .2877 2843 .3264 .3228 3192 .3632 .3594 3557 .4013 .3974 .3936 .4404 4364 .4325 .4801 .4761 .4721 .2514 2483 .2451 .2810 .2776 3156 .3121 .3520 .3483 3897 .3859 .4286 .4681 .4641 .4247
Transcribed Image Text:Number in the table represents P(Z≤2) z 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.6 .0002 .0002 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 -3.5 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 -3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 -3.0.0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 -2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 -2.3 .0107 0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 -2.1 .0179 .0174 0170 .0166 .0162 .0158 0154 .0150 0146 .0143 -2.0.0228 .0222 .0217 .0212 .0207 .0202 0197 .0192 0188 .0183 -1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 -1.8 .0359 -1.7 .0446 .0436 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 .1788 .1762 .1736 2061 .2033 .2005 -1.5 .0668 .0655 .0643 .0630 .0618 .0606 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 -1.3 .0968 .0951 .0934 .0918 .0901 .0885 -1.2 1151 .1131 .1112 .1093 .1075 .1056 -1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 -0.9 .1841 .1814 .1711 .1685 .1660 -0.8 2119 .2090 .0594 .0582 .0721 .0708 .0694 .0869 .0853 .0838 .0823 .1038 .1020 .1003 .0985 .0571 .0559 .0681 .1423 .1401 .1379 .1635 .1611 .1977 .1949 .1922 .1894 .1867 -0.7 .2420 2389 2358 .2327 .2296 .2266 2236 .2206 .2177 .2148 -0.6 .2743 2709 2676 2643 .2611 -0.5 .3085 3050 -0.4 .3446 3409 -0.3 .3821 .3783 -0.2 .4207 .4168 -0.1 .4602 .4562 -0.0 .5000 .4960 3015 .2981 .2946 .3372 .3336 .3300 .3745 .3707 .3669 4129 .4090 .4052 .4522 4483 4443 .4920 .4880 .4840 2578 2546 .2912 .2877 2843 .3264 .3228 3192 .3632 .3594 3557 .4013 .3974 .3936 .4404 4364 .4325 .4801 .4761 .4721 .2514 2483 .2451 .2810 .2776 3156 .3121 .3520 .3483 3897 .3859 .4286 .4681 .4641 .4247
2. Suppose that we are making an auto part and that the mean length of the part is 5 inches with a standard deviation of 0.25 inches, and the length is normally distributed. The upper specification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table is provided on the next page. a. What is the process capability index, Cpk?
Transcribed Image Text:2. Suppose that we are making an auto part and that the mean length of the part is 5 inches with a standard deviation of 0.25 inches, and the length is normally distributed. The upper specification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table is provided on the next page. a. What is the process capability index, Cpk?
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