In a company, the produced products are classified in four categories such as 1* quality, 2nd quality, 3rd quality, and 4ª quality according to one of its quality criteria (i.e., if the product is memory drive, then the quality criteria is speed of transferring data). The quality engineer uses the observations received from the products to estimate the normal parameters µ and o?, and then classifies them as the 1* class to those whose quality criteria score is greater than u + 6, 2nd class to those whose score is between u and u+o, 3rd class to those whose score is between u – o and H, 4ª class to those whose score is below u – o. Determine the percentages of the products classified in 1*, 2nd, 3rd and 4th class of quality, respectively. P(X Sz) = X- N(0, 1)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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In a company, the produced products are classified in four categories such as 1* quality,
2nd quality, 3rd quality, and 4th quality according to one of its quality criteria (i.e., if the product
is memory drive, then the quality criteria is speed of transferring data). The quality engineer
uses the observations received from the products to estimate the normal parameters u and o?,
and then classifies them as the 1* class to those whose quality criteria score is greater than u +
o, 2nd class to those whose score is between u and u + o, 3rd class to those whose score is
between u – o and µ, 4ª class to those whose score is below u – 0. Determine the percentages
of the products classified in 1", 2nd, 3rd and 4 class of quality, respectively.
P(X <z) =
p(t)dt
X ~ N(0, 1)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000 0.5040
0.5080
0.5120
0.5160
0.5239
0.5596 0.5636 0.5675
0.5199
0.5279
0.5319 0.5359
0.1
0.5398 0.5438
0.5478
0.5517 0.5557
0.5714
0.5753
0.2 0.5793 0.5832
0.5871
0.5910 0.5948
0.5987
0.6026 0.6064
0.6103 0.6141
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.6368
0.6406 0.6443
0.6480 0.6517
0.4
0.6554 0.6591 0.6628
0.6664 0.6700
0.6736
0.6772 0.6808
0.6844 0.6879
0.5
0.6
0.6915
0.6950 0.6985
0.7019
0.7054
0.7088
0.7123 0.7157
0.7190 0.7224
0.7257 0.7291
0.7324
0.7357 0.7389
0.7422
0.7454 0.7486
0.7517 0.7549
0.7
0.1580
0.7611
0.7642
0.7673 0.7704
0.7734
0.7764 0.7794
0.7823 0.7852
0.8 0.7881
0.7910
0.7939
0.7967 0.7995
0.8023
0.8051 0.8078
0.8106 0.8133
0.9
0.8159
0.8186
0.8212
0.8238
0.8264
0.8289
0.8315 0.8340
0.8365
0.8389
1.0
0.8413
0.8438
0.8461
0.8485 0.8508
0.8531
0.8554
0.8577
0.8599 0.8621
0.8643
0.8849 0.8869
0.8749
0.8944
0.8790
0.8962 0.8980
1.1
0.8665
0.8686
0.8708 0.8729
0.8770
0.8810
0.8830
1.2
0.8888
0.9066
0.8907 0.8925
0.8997
0.9015
1.3
0.9032 0.9049
0.9082
0.9099
0.9115
0.9131 0.9147
0.9162 0.9177
1.4
0.9192 0.9207
0.9222
0.9236 0.9251
0.9265
0.9279 0.9292
0.9306 0.9319
1.5
0.9332 0.9345
0.9357
0.9474 0.9484 0.9495
0.9370
0.9382
0.9394
0.9406 0.9418
0.9429 0.9441
1.6
0.9452 0.9463
0.9505
0.9515 0.9525 0.9535 0.9545
1.7
0.9554
0.9564
0.9573
0.9582 0.9591
0.9599
0.9608
0.9616
0.9625 0.9633
1.8
0.9641
0.9649
0.9656
0.9664 0.9671
0.9678
0.9686
0.9693
0.9699
0.9706
1.9
0.9713 0.9719
0.9726
0.9732
0.9738
0.9744
0.9750 0.9756
0.9761 0.9767
2.0
0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808
0.9812 0.9817
2.1
0.9821
0.9826
0.9830
0.9834
0.9838
0.9842 0.9846
0.9850
0.9854 0.9857
2.2
0.9861
0.9864 0.9868
0.9871
0.9875
0.9878
0.9881
0.9884
0.9887 0.9890
2.3
0.9893 0.9896
0.9898
0.9901.
0.9904
0.9906
0.9909 0.9911
0.9913 0.9916
2.4
0.9918 0.9920
0.9922
0.9925 0.9927 0.9929
0.9931
0.9932
0.9934 0.9936
2.5
0.9938
0.9940
0.9941
0.9943
0.9945
0.9946 0.9948 0.9949
0.9951
0.9952
2.6
0.9953
0.9955
0.9956
0.9957
0.9959
0.9900
0.9961
0.9962
0.9963 0.9964
2.7 0.9965 0.9966
0.9967
0.9968 0.9969
0.9970 0.9971 0.9972
0.9973 0.9974
2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978
0.9979 0.9979
0.9980 0.9981
2.9
0.9981
0.9982
0.9982
0.9983 0.9984
0.9984
0.9985 0.9985
0.9986 0.9986
3.0
0.9987
0.9987
0.9987
0.9988
0.9988
0.9989
0.9989
0.9989
0.9990 0.9990
si si si sNN S N NNS
Transcribed Image Text:In a company, the produced products are classified in four categories such as 1* quality, 2nd quality, 3rd quality, and 4th quality according to one of its quality criteria (i.e., if the product is memory drive, then the quality criteria is speed of transferring data). The quality engineer uses the observations received from the products to estimate the normal parameters u and o?, and then classifies them as the 1* class to those whose quality criteria score is greater than u + o, 2nd class to those whose score is between u and u + o, 3rd class to those whose score is between u – o and µ, 4ª class to those whose score is below u – 0. Determine the percentages of the products classified in 1", 2nd, 3rd and 4 class of quality, respectively. P(X <z) = p(t)dt X ~ N(0, 1) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5239 0.5596 0.5636 0.5675 0.5199 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.1580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.8643 0.8849 0.8869 0.8749 0.8944 0.8790 0.8962 0.8980 1.1 0.8665 0.8686 0.8708 0.8729 0.8770 0.8810 0.8830 1.2 0.8888 0.9066 0.8907 0.8925 0.8997 0.9015 1.3 0.9032 0.9049 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9474 0.9484 0.9495 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901. 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9900 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 si si si sNN S N NNS
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