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)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![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
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