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Math Help - Normal Distribution table

  1. #1
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    Normal Distribution table

    Hi,

    I have a question about looking up Normal Tables...

    I have a few steps that I do not understand. It would be great if someone explained..

    These are the steps done in my book..

    first step: N \left(\frac{-2.28-4\mu}{4}\right) = 0.1423

    second step: \left(\frac{-2.28-4\mu}{4}\right) = -1.07

    going from 1st to 2nd step, the RHS becomes -1.07. i tried looking up on the normal distribution table, but I was unsuccessful. Could anyone explain.? Thank you
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by serious331 View Post
    Hi,

    I have a question about looking up Normal Tables...

    I have a few steps that I do not understand. It would be great if someone explained..

    These are the steps done in my book..

    first step: N \left(\frac{-2.28-4\mu}{4}\right) = 0.1423

    second step: \left(\frac{-2.28-4\mu}{4}\right) = -1.07

    going from 1st to 2nd step, the RHS becomes -1.07. i tried looking up on the normal distribution table, but I was unsuccessful. Could anyone explain.? Thank you
    Look at the table at the bottom of the page:
    Normal Distribution - Pavement Interactive
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by serious331 View Post
    Hi,

    I have a question about looking up Normal Tables...

    I have a few steps that I do not understand. It would be great if someone explained..

    These are the steps done in my book..

    first step: N \left(\frac{-2.28-4\mu}{4}\right) = 0.1423

    second step: \left(\frac{-2.28-4\mu}{4}\right) = -1.07

    going from 1st to 2nd step, the RHS becomes -1.07. i tried looking up on the normal distribution table, but I was unsuccessful. Could anyone explain.? Thank you
    This would be more easily done by someone in person. Now it depends on what type of normal table you have. A common type is like the one below where the cumulative standard normal is given for positive z (which corresponds to P(z)>=0.5). If you have this form of table you need to exploit the symmetries of the normal distribution, which in this case tells you that:

    P(-|z|)=1-P(|z|)

    So you have P(z)=0.1423, as this is less than 0.5, we need to look up P(z*)=1-0.1423=0.8577. Looking this up we find z*=1.07, and so the required z=-z*=-1.07.

    (Looking up in this case is a reverse table look-up, which means you find the value you want to look up in the body of the table and read off the z value that gives this result)

    Code:
             Public Domain Normal Distribution Table 
     
                   Tables of the Normal Distribution 
    ------- FIRST TABLE:  PROBABILITY FROM -oo TO Z ------
            Probability Content
             from  -oo to Z
     
      Z | 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 0.5199 0.5239 0.5279 0.5319 0.5359
    0.1 | 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 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 | 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
    0.6 | 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
    0.7 | 0.7580 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
    1.1 | 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
    1.2 | 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
    1.3 | 0.9032 0.9049 0.9066 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 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
    1.6 | 0.9452 0.9463 0.9474 0.9484 0.9495 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 0.9960 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
     
    ------- SECOND TABLE:   FAR TAIL PROBABILITIES  ------
       Far Right
       Tail Probabilities
     
      Z  P{Z to oo} |   Z  P{Z to oo} |   Z  P{Z to oo}  |  Z    P{Z to oo}
    ----------------+-----------------+------------------+------------------
     2.0  0.02275   |  3.0 0.001350   |  4.0 0.00003167  |  5.0  2.867 E-7
     2.1  0.01786   |  3.1 0.0009676  |  4.1 0.00002066  |  5.5  1.899 E-8
     2.2  0.01390   |  3.2 0.0006871  |  4.2 0.00001335  |  6.0  9.866 E-10
     2.3  0.01072   |  3.3 0.0004834  |  4.3 0.00000854  |  6.5  4.016 E-11
     2.4  0.00820   |  3.4 0.0003369  |  4.4 0.000005413 |  7.0  1.280 E-12
     2.5  0.00621   |  3.5 0.0002326  |  4.5 0.000003398 |  7.5  3.191 E-14
     2.6  0.004661  |  3.6 0.0001591  |  4.6 0.000002112 |  8.0  6.221 E-16
     2.7  0.003467  |  3.7 0.0001078  |  4.7 0.000001300 |  8.5  9.480 E-18
     2.8  0.002555  |  3.8 0.00007235 |  4.8 7.933 E-7   |  9.0  1.129 E-19
     2.9  0.001866  |  3.9 0.00004810 |  4.9 4.792 E-7   |  9.5  1.049 E-21
     
      -----------------------------------------------------------------
      These tables are public domain.
      They are produced by APL programs written by the author William Knight
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