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 DISTRIBUTIONCUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTIONCumulativeEntries in the tablegive the area under thecurve to the left of thez value. For example, for2= 1.25, the cumulativeprobability is 8944.probabilityEntries in this tablegive the area under thecurve to the left of thez value. For example, for2=-85, the cumulativeCumulativeprobabilityprobability is .1977.0001020304.050203040506.07.08.090607.0809535952395636-3.0527953195080547800130013519951205517.001300120012 0011516050405438.0011001100100010500057536141651756755714610364805596539857935557-2.9-2.800190018.0018002400330017.0016 0016.0023.00150015.0014.001459105948598760266064S83262175871.26179655400260025002300220030002164436808002100206331.6700.0019.63686736625562936406-2.7-2.6.0035.00340032.0043.00570031004100290039.00280027.0026677268446879659166286664.0047.00450044.0040.00380037.00367157.71907224.7549-2.5.006270197357767379678238.0060.0059.71237054.738900550054005200510049.0048691569506985708875177422.7734257729173247454.7486-2.40082.008001040136.0078010200750071785281338389.0073.0069006877648051.0066006477947823764279397704.79958264.75807611-2.3-2.2-2.10107009901290166.0096.0094.009100890087008480238289807881067910S1860139013278810125016201220119011683650113014601108I5982128315834001790174017002170158 01540202 0197015001920143-2.00228857785998810.0222862185088729892590998531874989449115926585548770.0212020701880183LO8413843884618485S83090159177-1.902878643866586868708879002810274.026803360262.02560250 0244.0314 0307.02390233898091478997S8499032919289079082896291318888121.38869-1.8-1.7-1603590351.0344.0329.040903220301.03750465029403679049920790669222916293060446043604270418051606300401049504850606 0594.0392 03849251927992929319054805371.49236.05260643O5050475.O58204550559-150668065594299535.061893949505959996789744057194189441938294951.59332934593579370940694849582966495259616954596339515946395649649-14.08089474.079309510778.0764074907211.69452.073508850708069408381038 1020 1003.0681960896259591967109689573-1.3-1.209341.795540918109312920901107508690853.082396869750970697679693969996419713965697261151.1131I1121.81056125109851170137913579732973897569761-1.1-1097191335156213141.9.1271.149212301446.1210119015879817985715391515.1469981298541423 140197989842980897839830986898982.0972977897889793980398389875-9984698501841211998269864.1814.17881762.173698341711.19772.12.22.316851660 1635 16119821988499119887989098719901-89878988120902389206123582033200522961922.194918949861.18672177 214824832810991699069929-7242023279904990999139896226625782236989322062514-.6992799319932993499362743308527092676992099222643298199252611294625462451249918-5305030152912287728432776995299469960993899409941994399459948994999512.526996399739980996199649962997299799985-4-334463821340999579968337233369959330036693264322899559956319235573156312199539969997099743783997137454129A52237074090996736324013359439742.72.829996635203897348338599965-2420799799981997699824168997840524443997599779977393643259974-.14602998599869986A562A960448344049982998399849984436447614286468142479981-05000492048804840480147219990464199879989998999903.099879987998899889989

Name: The diameter of a mason jar is 3 inches but can be as large as 3.05 in
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Description: 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 o

In question, We have given upper control limit and lower control limit for mason jar and grand mean…

Answered: The diameter of a mason jar is 3 inches…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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