The diameter of a mason jar is 3 inches but can be as large as 3.05 inches and as small as 2.95 inches. Twenty-five samples of mason jars are taken and it is discovered that these components have a grand mean of 3.01 inches and a standard deviation of 0.03 inches. What is the Cpk value?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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The diameter of a mason jar is 3 inches but can be as large as 3.05 inches and as small as 2.95 inches. Twenty-five samples of mason jars are taken and it is discovered that these components have a grand mean of 3.01 inches and a standard deviation of 0.03 inches. What is the Cpk value? (4pts)

CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION
CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION
Cumulative
Entries in the table
give the area under the
curve to the left of the
z value. For example, for
2= 1.25, the cumulative
probability is 8944.
probability
Entries in this table
give the area under the
curve to the left of the
z value. For example, for
2=-85, the cumulative
Cumulative
probability
probability is .1977.
00
01
02
03
04
.05
02
03
04
05
06
.07
.08
.09
06
07
.08
09
5359
5239
5636
-3.0
5279
5319
5080
5478
0013
0013
5199
5120
5517
.0013
0012
0012 0011
5160
5040
5438
.0011
0011
0010
0010
5000
5753
6141
6517
5675
5714
6103
6480
5596
5398
5793
5557
-2.9
-2.8
0019
0018
.0018
0024
0033
0017
.0016 0016
.0023
.0015
0015
.0014
.0014
5910
5948
5987
6026
6064
S832
6217
5871
.2
6179
6554
0026
0025
0023
0022
0030
0021
6443
6808
0021
0020
6331
.6700
.0019
.6368
6736
6255
6293
6406
-2.7
-2.6
.0035
.0034
0032
.0043
.0057
0031
0041
0029
0039
.0028
0027
.0026
6772
6844
6879
6591
6628
6664
.0047
.0045
0044
.0040
.0038
0037
.0036
7157
.7190
7224
.7549
-2.5
.0062
7019
7357
7673
7967
8238
.0060
.0059
.7123
7054
.7389
0055
0054
0052
0051
0049
.0048
6915
6950
6985
7088
7517
7422
.7734
257
7291
7324
7454
.7486
-2.4
0082
.0080
0104
0136
.0078
0102
0075
0071
7852
8133
8389
.0073
.0069
0068
7764
8051
.0066
0064
7794
7823
7642
7939
7704
.7995
8264
.7580
7611
-2.3
-2.2
-2.1
0107
0099
0129
0166
.0096
.0094
.0091
0089
0087
0084
8023
8289
8078
8106
7910
S186
0139
0132
7881
0125
0162
0122
0119
0116
8365
0113
0146
0110
8I59
8212
8315
8340
0179
0174
0170
0217
0158 0154
0202 0197
0150
0192
0143
-2.0
0228
8577
8599
8810
.0222
8621
8508
8729
8925
9099
8531
8749
8944
9115
9265
8554
8770
.0212
0207
0188
0183
LO
8413
8438
8461
8485
S830
9015
9177
-1.9
0287
8643
8665
8686
8708
8790
0281
0274
.0268
0336
0262
.0256
0250 0244
.0314 0307
.0239
0233
8980
9147
8997
S849
9032
9192
8907
9082
8962
9131
8888
12
1.3
8869
-1.8
-1.7
-16
0359
0351
.0344
.0329
.0409
0322
0301
.0375
0465
0294
0367
9049
9207
9066
9222
9162
9306
0446
0436
0427
0418
0516
0630
0401
0495
0485
0606 0594
.0392 0384
9251
9279
9292
9319
0548
0537
1.4
9236
.0526
0643
O505
0475
.O582
0455
0559
-15
0668
0655
9429
9535
.0618
9394
9505
9599
9678
9744
0571
9418
9441
9382
9495
1.5
9332
9345
9357
9370
9406
9484
9582
9664
9525
9616
9545
9633
9515
9463
9564
9649
-14
.0808
9474
.0793
0951
0778
.0764
0749
0721
1.6
9452
.0735
0885
0708
0694
0838
1038 1020 1003
.0681
9608
9625
9591
9671
0968
9573
-1.3
-1.2
0934
1.7
9554
0918
1093
1292
0901
1075
0869
0853
.0823
9686
9750
9706
9767
9693
9699
9641
9713
9656
9726
1151
.1131
I112
1.8
1056
1251
0985
1170
1379
1357
9732
9738
9756
9761
-1.1
-10
9719
1335
1562
1314
1.9
.1271
.1492
1230
1446
.1210
1190
1587
9817
9857
1539
1515
.1469
9812
9854
1423 1401
9798
9842
9808
9783
9830
9868
9898
2.0
972
9778
9788
9793
9803
9838
9875
-9
9846
9850
1841
2119
9826
9864
.1814
.1788
1762
.1736
9834
1711
.1977
2.1
2.2
2.3
1685
1660 1635 1611
9821
9884
9911
9887
9890
9871
9901
-8
9878
9881
2090
2389
2061
2358
2033
2005
2296
1922
.1949
1894
9861
.1867
2177 2148
2483
2810
9916
9906
9929
-7
2420
2327
9904
9909
9913
9896
2266
2578
2236
9893
2206
2514
-.6
9927
9931
9932
9934
9936
2743
3085
2709
2676
9920
9922
2643
2981
9925
2611
2946
2546
2451
24
9918
-5
3050
3015
2912
2877
2843
2776
9952
9946
9960
9938
9940
9941
9943
9945
9948
9949
9951
2.5
26
9963
9973
9980
9961
9964
9962
9972
9979
9985
-4
-3
3446
3821
3409
9957
9968
3372
3336
9959
3300
3669
3264
3228
9955
9956
3192
3557
3156
3121
9953
9969
9970
9974
3783
9971
3745
4129
A522
3707
4090
9967
3632
4013
3594
3974
2.7
2.8
29
9966
3520
3897
3483
3859
9965
-2
4207
9979
9981
9976
9982
4168
9978
4052
4443
9975
9977
9977
3936
4325
9974
-.1
4602
9985
9986
9986
A562
A960
4483
4404
9982
9983
9984
9984
4364
4761
4286
4681
4247
9981
-0
5000
4920
4880
4840
4801
4721
9990
4641
9987
9989
9989
9990
3.0
9987
9987
9988
9988
9989
Transcribed Image Text:CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative Entries in the table give the area under the curve to the left of the z value. For example, for 2= 1.25, the cumulative probability is 8944. probability Entries in this table give the area under the curve to the left of the z value. For example, for 2=-85, the cumulative Cumulative probability probability is .1977. 00 01 02 03 04 .05 02 03 04 05 06 .07 .08 .09 06 07 .08 09 5359 5239 5636 -3.0 5279 5319 5080 5478 0013 0013 5199 5120 5517 .0013 0012 0012 0011 5160 5040 5438 .0011 0011 0010 0010 5000 5753 6141 6517 5675 5714 6103 6480 5596 5398 5793 5557 -2.9 -2.8 0019 0018 .0018 0024 0033 0017 .0016 0016 .0023 .0015 0015 .0014 .0014 5910 5948 5987 6026 6064 S832 6217 5871 .2 6179 6554 0026 0025 0023 0022 0030 0021 6443 6808 0021 0020 6331 .6700 .0019 .6368 6736 6255 6293 6406 -2.7 -2.6 .0035 .0034 0032 .0043 .0057 0031 0041 0029 0039 .0028 0027 .0026 6772 6844 6879 6591 6628 6664 .0047 .0045 0044 .0040 .0038 0037 .0036 7157 .7190 7224 .7549 -2.5 .0062 7019 7357 7673 7967 8238 .0060 .0059 .7123 7054 .7389 0055 0054 0052 0051 0049 .0048 6915 6950 6985 7088 7517 7422 .7734 257 7291 7324 7454 .7486 -2.4 0082 .0080 0104 0136 .0078 0102 0075 0071 7852 8133 8389 .0073 .0069 0068 7764 8051 .0066 0064 7794 7823 7642 7939 7704 .7995 8264 .7580 7611 -2.3 -2.2 -2.1 0107 0099 0129 0166 .0096 .0094 .0091 0089 0087 0084 8023 8289 8078 8106 7910 S186 0139 0132 7881 0125 0162 0122 0119 0116 8365 0113 0146 0110 8I59 8212 8315 8340 0179 0174 0170 0217 0158 0154 0202 0197 0150 0192 0143 -2.0 0228 8577 8599 8810 .0222 8621 8508 8729 8925 9099 8531 8749 8944 9115 9265 8554 8770 .0212 0207 0188 0183 LO 8413 8438 8461 8485 S830 9015 9177 -1.9 0287 8643 8665 8686 8708 8790 0281 0274 .0268 0336 0262 .0256 0250 0244 .0314 0307 .0239 0233 8980 9147 8997 S849 9032 9192 8907 9082 8962 9131 8888 12 1.3 8869 -1.8 -1.7 -16 0359 0351 .0344 .0329 .0409 0322 0301 .0375 0465 0294 0367 9049 9207 9066 9222 9162 9306 0446 0436 0427 0418 0516 0630 0401 0495 0485 0606 0594 .0392 0384 9251 9279 9292 9319 0548 0537 1.4 9236 .0526 0643 O505 0475 .O582 0455 0559 -15 0668 0655 9429 9535 .0618 9394 9505 9599 9678 9744 0571 9418 9441 9382 9495 1.5 9332 9345 9357 9370 9406 9484 9582 9664 9525 9616 9545 9633 9515 9463 9564 9649 -14 .0808 9474 .0793 0951 0778 .0764 0749 0721 1.6 9452 .0735 0885 0708 0694 0838 1038 1020 1003 .0681 9608 9625 9591 9671 0968 9573 -1.3 -1.2 0934 1.7 9554 0918 1093 1292 0901 1075 0869 0853 .0823 9686 9750 9706 9767 9693 9699 9641 9713 9656 9726 1151 .1131 I112 1.8 1056 1251 0985 1170 1379 1357 9732 9738 9756 9761 -1.1 -10 9719 1335 1562 1314 1.9 .1271 .1492 1230 1446 .1210 1190 1587 9817 9857 1539 1515 .1469 9812 9854 1423 1401 9798 9842 9808 9783 9830 9868 9898 2.0 972 9778 9788 9793 9803 9838 9875 -9 9846 9850 1841 2119 9826 9864 .1814 .1788 1762 .1736 9834 1711 .1977 2.1 2.2 2.3 1685 1660 1635 1611 9821 9884 9911 9887 9890 9871 9901 -8 9878 9881 2090 2389 2061 2358 2033 2005 2296 1922 .1949 1894 9861 .1867 2177 2148 2483 2810 9916 9906 9929 -7 2420 2327 9904 9909 9913 9896 2266 2578 2236 9893 2206 2514 -.6 9927 9931 9932 9934 9936 2743 3085 2709 2676 9920 9922 2643 2981 9925 2611 2946 2546 2451 24 9918 -5 3050 3015 2912 2877 2843 2776 9952 9946 9960 9938 9940 9941 9943 9945 9948 9949 9951 2.5 26 9963 9973 9980 9961 9964 9962 9972 9979 9985 -4 -3 3446 3821 3409 9957 9968 3372 3336 9959 3300 3669 3264 3228 9955 9956 3192 3557 3156 3121 9953 9969 9970 9974 3783 9971 3745 4129 A522 3707 4090 9967 3632 4013 3594 3974 2.7 2.8 29 9966 3520 3897 3483 3859 9965 -2 4207 9979 9981 9976 9982 4168 9978 4052 4443 9975 9977 9977 3936 4325 9974 -.1 4602 9985 9986 9986 A562 A960 4483 4404 9982 9983 9984 9984 4364 4761 4286 4681 4247 9981 -0 5000 4920 4880 4840 4801 4721 9990 4641 9987 9989 9989 9990 3.0 9987 9987 9988 9988 9989
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