Three probability distributions will be used in this course. Different textbooks use different methods to construct these tables. To avoid confusion, I create the following distribution tables using the same methods as used in Navidi’s textbook.

This document was created using R Markdown via R Studio.

Normal Table

Standard normal table based on the left-tail probability
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
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

t-distribution Table

Unlike the normal table that contains probabilities in the main body of the table, t distribution givens the quantiles based on select degrees of freedom and right tail probabilities.

d.f 0.4000 0.2500 0.1000 0.0500 0.0250 0.0100 0.0050 0.0025 0.0010 0.0005
1 0.3249 1.0000 3.078 6.314 12.706 31.820 63.657 127.321 318.309 636.619
2 0.2887 0.8165 1.886 2.920 4.303 6.965 9.925 14.089 22.327 31.599
3 0.2767 0.7649 1.638 2.353 3.182 4.541 5.841 7.453 10.214 12.924
4 0.2707 0.7407 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610
5 0.2672 0.7267 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869
6 0.2648 0.7176 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5.959
7 0.2632 0.7111 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.408
8 0.2619 0.7064 1.397 1.859 2.306 2.897 3.355 3.833 4.501 5.041
9 0.2610 0.7027 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.781
10 0.2602 0.6998 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.587
11 0.2596 0.6974 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.437
12 0.2590 0.6955 1.356 1.782 2.179 2.681 3.054 3.428 3.930 4.318
13 0.2586 0.6938 1.350 1.771 2.160 2.650 3.012 3.373 3.852 4.221
14 0.2582 0.6924 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.141
15 0.2579 0.6912 1.341 1.753 2.131 2.603 2.947 3.286 3.733 4.073
16 0.2576 0.6901 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.015
17 0.2573 0.6892 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3.965
18 0.2571 0.6884 1.330 1.734 2.101 2.552 2.878 3.197 3.611 3.922
19 0.2569 0.6876 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883
20 0.2567 0.6870 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.849
21 0.2566 0.6864 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.819
22 0.2564 0.6858 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.792
23 0.2563 0.6853 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.768
24 0.2562 0.6848 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.745
25 0.2561 0.6844 1.316 1.708 2.059 2.485 2.787 3.078 3.450 3.725
26 0.2560 0.6840 1.315 1.706 2.055 2.479 2.779 3.067 3.435 3.707
27 0.2559 0.6837 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.690
28 0.2558 0.6834 1.312 1.701 2.048 2.467 2.763 3.047 3.408 3.674
29 0.2557 0.6830 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.659
30 0.2556 0.6828 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646
31 0.2555 0.6825 1.310 1.696 2.039 2.453 2.744 3.022 3.375 3.634
32 0.2555 0.6822 1.309 1.694 2.037 2.449 2.739 3.015 3.365 3.622
33 0.2554 0.6820 1.308 1.692 2.034 2.445 2.733 3.008 3.356 3.611
34 0.2553 0.6818 1.307 1.691 2.032 2.441 2.728 3.002 3.348 3.601
35 0.2553 0.6816 1.306 1.690 2.030 2.438 2.724 2.996 3.340 3.591
36 0.2552 0.6814 1.306 1.688 2.028 2.434 2.720 2.990 3.333 3.582
37 0.2552 0.6812 1.305 1.687 2.026 2.431 2.715 2.985 3.326 3.574
38 0.2551 0.6810 1.304 1.686 2.024 2.429 2.712 2.980 3.319 3.566
39 0.2551 0.6808 1.304 1.685 2.023 2.426 2.708 2.976 3.313 3.558
40 0.2550 0.6807 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3.551
41 0.2550 0.6805 1.302 1.683 2.019 2.421 2.701 2.967 3.301 3.544
42 0.2550 0.6804 1.302 1.682 2.018 2.418 2.698 2.963 3.296 3.538
43 0.2549 0.6802 1.302 1.681 2.017 2.416 2.695 2.959 3.291 3.532
44 0.2549 0.6801 1.301 1.680 2.015 2.414 2.692 2.955 3.286 3.526
45 0.2549 0.6800 1.301 1.679 2.014 2.412 2.690 2.952 3.281 3.520
46 0.2548 0.6799 1.300 1.679 2.013 2.410 2.687 2.949 3.277 3.515
47 0.2548 0.6797 1.300 1.678 2.012 2.408 2.685 2.946 3.273 3.510
48 0.2548 0.6796 1.299 1.677 2.011 2.407 2.682 2.943 3.269 3.505
49 0.2547 0.6795 1.299 1.677 2.010 2.405 2.680 2.940 3.265 3.500
50 0.2547 0.6794 1.299 1.676 2.009 2.403 2.678 2.937 3.261 3.496
51 0.2547 0.6793 1.298 1.675 2.008 2.402 2.676 2.934 3.258 3.492
52 0.2546 0.6792 1.298 1.675 2.007 2.400 2.674 2.932 3.255 3.488
53 0.2546 0.6791 1.298 1.674 2.006 2.399 2.672 2.929 3.251 3.484
54 0.2546 0.6791 1.297 1.674 2.005 2.397 2.670 2.927 3.248 3.480
55 0.2546 0.6790 1.297 1.673 2.004 2.396 2.668 2.925 3.245 3.476
56 0.2546 0.6789 1.297 1.673 2.003 2.395 2.667 2.922 3.242 3.473
57 0.2545 0.6788 1.297 1.672 2.002 2.394 2.665 2.920 3.240 3.470
58 0.2545 0.6787 1.296 1.672 2.002 2.392 2.663 2.918 3.237 3.466
59 0.2545 0.6787 1.296 1.671 2.001 2.391 2.662 2.916 3.234 3.463
60 0.2545 0.6786 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.460
61 0.2545 0.6785 1.296 1.670 2.000 2.389 2.659 2.913 3.229 3.457
62 0.2544 0.6785 1.295 1.670 1.999 2.388 2.658 2.911 3.227 3.454
63 0.2544 0.6784 1.295 1.669 1.998 2.387 2.656 2.909 3.225 3.452
64 0.2544 0.6783 1.295 1.669 1.998 2.386 2.655 2.908 3.223 3.449
65 0.2544 0.6783 1.295 1.669 1.997 2.385 2.654 2.906 3.220 3.447
66 0.2544 0.6782 1.294 1.668 1.997 2.384 2.652 2.905 3.218 3.444
67 0.2544 0.6782 1.294 1.668 1.996 2.383 2.651 2.903 3.216 3.442
68 0.2543 0.6781 1.294 1.668 1.996 2.382 2.650 2.901 3.215 3.439
69 0.2543 0.6781 1.294 1.667 1.995 2.382 2.649 2.900 3.213 3.437
70 0.2543 0.6780 1.294 1.667 1.994 2.381 2.648 2.899 3.211 3.435
71 0.2543 0.6780 1.294 1.667 1.994 2.380 2.647 2.897 3.209 3.433
72 0.2543 0.6779 1.293 1.666 1.994 2.379 2.646 2.896 3.207 3.431
73 0.2543 0.6779 1.293 1.666 1.993 2.378 2.645 2.895 3.206 3.429
74 0.2543 0.6778 1.293 1.666 1.992 2.378 2.644 2.894 3.204 3.427
75 0.2542 0.6778 1.293 1.665 1.992 2.377 2.643 2.892 3.203 3.425
76 0.2542 0.6777 1.293 1.665 1.992 2.376 2.642 2.891 3.201 3.423
77 0.2542 0.6777 1.293 1.665 1.991 2.376 2.641 2.890 3.200 3.421
78 0.2542 0.6776 1.292 1.665 1.991 2.375 2.640 2.889 3.198 3.420
79 0.2542 0.6776 1.292 1.664 1.990 2.374 2.639 2.888 3.197 3.418
80 0.2542 0.6776 1.292 1.664 1.990 2.374 2.639 2.887 3.195 3.416
81 0.2542 0.6775 1.292 1.664 1.990 2.373 2.638 2.886 3.194 3.415
82 0.2542 0.6775 1.292 1.664 1.989 2.373 2.637 2.885 3.193 3.413
83 0.2542 0.6775 1.292 1.663 1.989 2.372 2.636 2.884 3.191 3.412
84 0.2542 0.6774 1.292 1.663 1.989 2.372 2.636 2.883 3.190 3.410
85 0.2541 0.6774 1.292 1.663 1.988 2.371 2.635 2.882 3.189 3.409
86 0.2541 0.6774 1.292 1.663 1.988 2.370 2.634 2.881 3.188 3.407
87 0.2541 0.6773 1.291 1.663 1.988 2.370 2.634 2.880 3.187 3.406
88 0.2541 0.6773 1.291 1.662 1.987 2.369 2.633 2.880 3.185 3.405
89 0.2541 0.6773 1.291 1.662 1.987 2.369 2.632 2.879 3.184 3.403
90 0.2541 0.6772 1.291 1.662 1.987 2.369 2.632 2.878 3.183 3.402
91 0.2541 0.6772 1.291 1.662 1.986 2.368 2.631 2.877 3.182 3.401
92 0.2541 0.6772 1.291 1.662 1.986 2.368 2.630 2.876 3.181 3.399
93 0.2541 0.6771 1.291 1.661 1.986 2.367 2.630 2.876 3.180 3.398
94 0.2541 0.6771 1.291 1.661 1.986 2.367 2.629 2.875 3.179 3.397
95 0.2541 0.6771 1.290 1.661 1.985 2.366 2.629 2.874 3.178 3.396
96 0.2541 0.6771 1.290 1.661 1.985 2.366 2.628 2.873 3.177 3.395
97 0.2540 0.6770 1.290 1.661 1.985 2.365 2.627 2.873 3.176 3.394
98 0.2540 0.6770 1.290 1.661 1.984 2.365 2.627 2.872 3.175 3.393
99 0.2540 0.6770 1.290 1.660 1.984 2.365 2.626 2.871 3.175 3.392
100 0.2540 0.6770 1.290 1.660 1.984 2.364 2.626 2.871 3.174 3.390

\(\chi^2\) Distribution Table

This \(\chi^2\) distribution table will be used for the hypothesis of independence test and the goodness of fit in last part of this course. The structure of this \(\chi^2\) is similar to that of the t-table. The main body has quantiles calculated based on various degrees of freedom and the right tail probability as used in Navidi’s textbook.

d.f 0.9950 0.9900 0.9750 0.9500 0.9000 0.1000 0.0500 0.0250 0.0100 0.0050
1 0.0000 0.0002 0.0010 0.0039 0.0158 2.705 3.841 5.024 6.635 7.879
2 0.0100 0.0201 0.0506 0.1026 0.2107 4.605 5.992 7.378 9.210 10.597
3 0.0717 0.1148 0.2158 0.3518 0.5844 6.251 7.815 9.348 11.345 12.838
4 0.2070 0.2971 0.4844 0.7107 1.0636 7.779 9.488 11.143 13.277 14.860
5 0.4117 0.5543 0.8312 1.1455 1.6103 9.236 11.070 12.832 15.086 16.750
6 0.6757 0.8721 1.2373 1.6354 2.2041 10.645 12.592 14.449 16.812 18.548
7 0.9893 1.2390 1.6899 2.1673 2.8331 12.017 14.067 16.013 18.475 20.278
8 1.3444 1.6465 2.1797 2.7326 3.4895 13.362 15.507 17.535 20.090 21.955
9 1.7349 2.0879 2.7004 3.3251 4.1682 14.684 16.919 19.023 21.666 23.589
10 2.1559 2.5582 3.2470 3.9403 4.8652 15.987 18.307 20.483 23.209 25.188
11 2.6032 3.0535 3.8157 4.5748 5.5778 17.275 19.675 21.920 24.725 26.757
12 3.0738 3.5706 4.4038 5.2260 6.3038 18.549 21.026 23.337 26.217 28.299
13 3.5650 4.1069 5.0088 5.8919 7.0415 19.812 22.362 24.736 27.688 29.820
14 4.0747 4.6604 5.6287 6.5706 7.7895 21.064 23.685 26.119 29.141 31.319
15 4.6009 5.2293 6.2621 7.2609 8.5468 22.307 24.996 27.488 30.578 32.801
16 5.1422 5.8122 6.9077 7.9616 9.3122 23.542 26.296 28.845 32.000 34.267
17 5.6972 6.4078 7.5642 8.6718 10.0852 24.769 27.587 30.191 33.409 35.718
18 6.2648 7.0149 8.2307 9.3905 10.8649 25.989 28.869 31.526 34.805 37.157
19 6.8440 7.6327 8.9065 10.1170 11.6509 27.204 30.143 32.852 36.191 38.582
20 7.4338 8.2604 9.5908 10.8508 12.4426 28.412 31.410 34.170 37.566 39.997
21 8.0337 8.8972 10.2829 11.5913 13.2396 29.615 32.671 35.479 38.932 41.401
22 8.6427 9.5425 10.9823 12.3380 14.0415 30.813 33.924 36.781 40.289 42.796
23 9.2604 10.1957 11.6886 13.0905 14.8480 32.007 35.172 38.076 41.638 44.181
24 9.8862 10.8564 12.4012 13.8484 15.6587 33.196 36.415 39.364 42.980 45.559
25 10.5197 11.5240 13.1197 14.6114 16.4734 34.382 37.653 40.647 44.314 46.928
26 11.1602 12.1981 13.8439 15.3792 17.2919 35.563 38.885 41.923 45.642 48.290
27 11.8076 12.8785 14.5734 16.1514 18.1139 36.741 40.113 43.194 46.963 49.645
28 12.4613 13.5647 15.3079 16.9279 18.9392 37.916 41.337 44.461 48.278 50.993
29 13.1211 14.2565 16.0471 17.7084 19.7677 39.087 42.557 45.722 49.588 52.336
30 13.7867 14.9535 16.7908 18.4927 20.5992 40.256 43.773 46.979 50.892 53.672
31 14.4578 15.6555 17.5387 19.2806 21.4336 41.422 44.985 48.232 52.191 55.003
32 15.1340 16.3622 18.2908 20.0719 22.2706 42.585 46.194 49.480 53.486 56.328
33 15.8153 17.0735 19.0467 20.8665 23.1102 43.745 47.400 50.725 54.776 57.648
34 16.5013 17.7891 19.8063 21.6643 23.9523 44.903 48.602 51.966 56.061 58.964
35 17.1918 18.5089 20.5694 22.4650 24.7967 46.059 49.802 53.203 57.342 60.275
36 17.8867 19.2327 21.3359 23.2686 25.6433 47.212 50.998 54.437 58.619 61.581
37 18.5858 19.9602 22.1056 24.0749 26.4921 48.363 52.192 55.668 59.892 62.883
38 19.2889 20.6914 22.8785 24.8839 27.3430 49.513 53.383 56.895 61.162 64.181
39 19.9959 21.4262 23.6543 25.6954 28.1958 50.660 54.572 58.120 62.428 65.476
40 20.7065 22.1643 24.4330 26.5093 29.0505 51.805 55.758 59.342 63.691 66.766
41 21.4208 22.9056 25.2145 27.3256 29.9071 52.949 56.942 60.561 64.950 68.053
42 22.1385 23.6501 25.9987 28.1440 30.7654 54.090 58.124 61.777 66.206 69.336
43 22.8595 24.3976 26.7854 28.9647 31.6255 55.230 59.303 62.990 67.459 70.616
44 23.5837 25.1480 27.5746 29.7875 32.4871 56.368 60.481 64.201 68.710 71.893
45 24.3110 25.9013 28.3662 30.6123 33.3504 57.505 61.656 65.410 69.957 73.166
46 25.0413 26.6572 29.1601 31.4390 34.2152 58.641 62.830 66.617 71.201 74.436
47 25.7746 27.4158 29.9562 32.2676 35.0814 59.774 64.001 67.821 72.443 75.704
48 26.5106 28.1770 30.7545 33.0981 35.9491 60.907 65.171 69.023 73.683 76.969
49 27.2493 28.9406 31.5549 33.9303 36.8182 62.038 66.339 70.222 74.919 78.231
50 27.9907 29.7067 32.3574 34.7643 37.6886 63.167 67.505 71.420 76.154 79.490
51 28.7347 30.4750 33.1618 35.5999 38.5604 64.295 68.669 72.616 77.386 80.747
52 29.4812 31.2457 33.9681 36.4371 39.4334 65.422 69.832 73.810 78.616 82.001
53 30.2300 32.0185 34.7763 37.2759 40.3076 66.548 70.993 75.002 79.843 83.253
54 30.9813 32.7934 35.5863 38.1162 41.1830 67.673 72.153 76.192 81.069 84.502
55 31.7348 33.5705 36.3981 38.9580 42.0596 68.796 73.311 77.380 82.292 85.749
56 32.4905 34.3495 37.2116 39.8013 42.9373 69.918 74.468 78.567 83.513 86.994
57 33.2484 35.1305 38.0267 40.6459 43.8161 71.040 75.624 79.752 84.733 88.236
58 34.0084 35.9135 38.8435 41.4920 44.6960 72.160 76.778 80.936 85.950 89.477
59 34.7704 36.6982 39.6619 42.3393 45.5770 73.279 77.930 82.117 87.166 90.715
60 35.5345 37.4849 40.4817 43.1880 46.4589 74.397 79.082 83.298 88.379 91.952
61 36.3005 38.2732 41.3031 44.0379 47.3418 75.514 80.232 84.476 89.591 93.186
62 37.0684 39.0633 42.1260 44.8890 48.2257 76.630 81.381 85.654 90.802 94.419
63 37.8382 39.8551 42.9503 45.7414 49.1105 77.745 82.529 86.830 92.010 95.649
64 38.6098 40.6486 43.7760 46.5949 49.9963 78.860 83.675 88.004 93.217 96.878
65 39.3831 41.4436 44.6030 47.4496 50.8829 79.973 84.821 89.177 94.422 98.105
66 40.1582 42.2402 45.4314 48.3054 51.7705 81.085 85.965 90.349 95.626 99.330
67 40.9350 43.0384 46.2610 49.1623 52.6588 82.197 87.108 91.519 96.828 100.554
68 41.7135 43.8380 47.0920 50.0202 53.5481 83.308 88.250 92.689 98.028 101.776
69 42.4935 44.6392 47.9242 50.8792 54.4381 84.418 89.391 93.856 99.228 102.996
70 43.2752 45.4417 48.7576 51.7393 55.3289 85.527 90.531 95.023 100.425 104.215
71 44.0584 46.2457 49.5922 52.6003 56.2206 86.635 91.670 96.189 101.621 105.432
72 44.8431 47.0510 50.4279 53.4623 57.1129 87.743 92.808 97.353 102.816 106.648
73 45.6293 47.8577 51.2648 54.3253 58.0061 88.850 93.945 98.516 104.010 107.862
74 46.4170 48.6657 52.1028 55.1892 58.9000 89.956 95.082 99.678 105.202 109.074
75 47.2060 49.4750 52.9419 56.0541 59.7946 91.061 96.217 100.839 106.393 110.286
76 47.9965 50.2856 53.7821 56.9198 60.6899 92.166 97.351 101.999 107.582 111.495
77 48.7884 51.0974 54.6234 57.7864 61.5858 93.270 98.484 103.158 108.771 112.704
78 49.5816 51.9104 55.4656 58.6539 62.4825 94.374 99.617 104.316 109.958 113.911
79 50.3761 52.7247 56.3089 59.5223 63.3799 95.476 100.749 105.473 111.144 115.117
80 51.1719 53.5401 57.1532 60.3915 64.2778 96.578 101.879 106.629 112.329 116.321
81 51.9690 54.3566 57.9984 61.2615 65.1765 97.680 103.010 107.783 113.512 117.524
82 52.7674 55.1743 58.8446 62.1323 66.0757 98.780 104.139 108.937 114.695 118.726
83 53.5669 55.9931 59.6918 63.0039 66.9756 99.880 105.267 110.090 115.876 119.927
84 54.3677 56.8130 60.5398 63.8763 67.8761 100.980 106.395 111.242 117.056 121.126
85 55.1696 57.6339 61.3888 64.7494 68.7772 102.079 107.522 112.393 118.236 122.325
86 55.9727 58.4559 62.2386 65.6233 69.6788 103.177 108.648 113.544 119.414 123.522
87 56.7769 59.2790 63.0894 66.4979 70.5810 104.275 109.773 114.693 120.591 124.718
88 57.5823 60.1030 63.9409 67.3732 71.4838 105.372 110.898 115.841 121.767 125.912
89 58.3888 60.9281 64.7934 68.2493 72.3872 106.469 112.022 116.989 122.942 127.106
90 59.1963 61.7541 65.6466 69.1260 73.2911 107.565 113.145 118.136 124.116 128.299
91 60.0049 62.5811 66.5007 70.0035 74.1955 108.661 114.268 119.282 125.290 129.490
92 60.8146 63.4090 67.3556 70.8816 75.1005 109.756 115.390 120.427 126.462 130.681
93 61.6253 64.2379 68.2112 71.7603 76.0060 110.850 116.511 121.572 127.633 131.871
94 62.4370 65.0677 69.0677 72.6398 76.9119 111.944 117.632 122.715 128.803 133.059
95 63.2496 65.8984 69.9249 73.5198 77.8184 113.038 118.752 123.858 129.973 134.246
96 64.0633 66.7299 70.7828 74.4005 78.7254 114.131 119.871 125.000 131.141 135.433
97 64.8780 67.5624 71.6415 75.2819 79.6329 115.223 120.990 126.141 132.309 136.619
98 65.6936 68.3957 72.5009 76.1638 80.5408 116.315 122.108 127.282 133.476 137.803
99 66.5101 69.2299 73.3611 77.0463 81.4493 117.407 123.225 128.422 134.642 138.987
100 67.3276 70.0649 74.2219 77.9295 82.3581 118.498 124.342 129.561 135.807 140.169