Cumulative Standard Normal Distribution Table

Department of Mathematics, Sinclair Community College, Dayton, OH

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

-0.00 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.10 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.20 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.30 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.40 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.50 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.60 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.70 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.80 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.90 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -1.00 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.10 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.20 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.30 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.40 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.50 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.60 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.70 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.80 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.90 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -2.00 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.10 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.20 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.30 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.40 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.50 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.60 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.70 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.80 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.90 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -3.00 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.10 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.20 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.30 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.40 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.50 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 -3.60 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.70 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.80 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

*Note: z-values less than -3.89 produce a probability of zero.

Cumulative Standard Normal Distribution Table

Department of Mathematics, Sinclair Community College, Dayton, OH

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.00 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.10 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.20 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.30 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.40 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.50 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.60 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.70 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.80 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.90 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.00 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.10 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.20 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.30 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.40 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.50 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.60 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.70 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.80 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.90 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.00 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.10 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.20 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.30 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.40 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.50 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.60 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.70 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.80 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.90 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.00 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.10 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.20 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.30 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.40 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.50 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.60 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.70 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.80 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

*Note: z-values greater than 3.89 produce a probability of one.

- 16 -

Tabulated values of the error functionerf(x) = 2 pi

x

0 ey2 dy

x erf x x erf x x erf x x erf x0.00 0.000000 0.40 0.428392 0.80 0.742101 1.20 0.9103140.01 0.011283 0.41 0.437969 0.81 0.748003 1.21 0.9129560.02 0.022565 0.42 0.447468 0.82 0.753811 1.22 0.9155340.03 0.033841 0.43 0.456887 0.83 0.759524 1.23 0.9180500.04 0.045111 0.44 0.466225 0.84 0.765143 1.24 0.9205050.05 0.056372 0.45 0.475482 0.85 0.770668 1.25 0.9229000.06 0.067622 0.46 0.484655 0.86 0.776100 1.26 0.9252360.07 0.078858 0.47 0.493745 0.87 0.781440 1.27 0.9275140.08 0.090078 0.48 0.502750 0.88 0.786687 1.28 0.9297340.09 0.101282 0.49 0.511668 0.89 0.791843 1.29 0.9318990.10 0.112463 0.50 0.520500 0.90 0.796908 1.30 0.9340080.11 0.123623 0.51 0.529244 0.91 0.801883 1.31 0.9360630.12 0.134758 0.52 0.537899 0.92 0.806768 1.32 0.9380650.13 0.145867 0.53 0.546464 0.93 0.811564 1.33 0.9400150.14 0.156947 0.54 0.554939 0.94 0.816271 1.34 0.9419140.15 0.167996 0.55 0.563323 0.95 0.820891 1.35 0.9437620.16 0.179012 0.56 0.571616 0.96 0.825424 1.36 0.9455610.17 0.189992 0.57 0.579816 0.97 0.829870 1.37 0.9473120.18 0.200936 0.58 0.587923 0.98 0.834232 1.38 0.9490160.19 0.211840 0.59 0.595936 0.99 0.838508 1.39 0.9506730.20 0.222703 0.60 0.603856 1.00 0.842701 1.40 0.9522850.21 0.233522 0.61 0.611681 1.01 0.846810 1.41 0.9538520.22 0.244296 0.62 0.619411 1.02 0.850838 1.42 0.9553760.23 0.255023 0.63 0.627046 1.03 0.854784 1.43 0.9568570.24 0.265700 0.64 0.634586 1.04 0.858650 1.44 0.9582970.25 0.276326 0.65 0.642029 1.05 0.862436 1.45 0.9596950.26 0.286900 0.66 0.649377 1.06 0.866144 1.46 0.9610540.27 0.297418 0.67 0.656628 1.07 0.869773 1.47 0.9623730.28 0.307880 0.68 0.663782 1.08 0.873326 1.48 0.9636540.29 0.318283 0.69 0.670840 1.09 0.876803 1.49 0.9648980.30 0.328627 0.70 0.677801 1.10 0.880205 1.50 0.9661050.31 0.338908 0.71 0.684666 1.11 0.883533 1.51 0.9672770.32 0.349126 0.72 0.691433 1.12 0.886788 1.52 0.9684130.33 0.359279 0.73 0.698104 1.13 0.889971 1.53 0.9695160.34 0.369365 0.74 0.704678 1.14 0.893082 1.54 0.9705860.35 0.379382 0.75 0.711156 1.15 0.896124 1.55 0.9716230.36 0.389330 0.76 0.717537 1.16 0.899096 1.56 0.9726280.37 0.399206 0.77 0.723822 1.17 0.902000 1.57 0.9736030.38 0.409009 0.78 0.730010 1.18 0.904837 1.58 0.9745470.39 0.418739 0.79 0.736103 1.19 0.907608 1.59 0.975462

- 17 -

x erf x x erf x x erf x x erf x1.60 0.976348 2.10 0.997021 2.60 0.999764 3.10 0.999988351.61 0.977207 2.11 0.997155 2.61 0.999777 3.11 0.999989081.62 0.978038 2.12 0.997284 2.62 0.999789 3.12 0.999989771.63 0.978843 2.13 0.997407 2.63 0.999800 3.13 0.999990421.64 0.979622 2.14 0.997525 2.64 0.999811 3.14 0.999991031.65 0.980376 2.15 0.997639 2.65 0.999822 3.15 0.999991601.66 0.981105 2.16 0.997747 2.66 0.999831 3.16 0.999992141.67 0.981810 2.17 0.997851 2.67 0.999841 3.17 0.999992641.68 0.982493 2.18 0.997951 2.68 0.999849 3.18 0.999993111.69 0.983153 2.19 0.998046 2.69 0.999858 3.19 0.999993561.70 0.983790 2.20 0.998137 2.70 0.999866 3.20 0.999993971.71 0.984407 2.21 0.998224 2.71 0.999873 3.21 0.999994361.72 0.985003 2.22 0.998308 2.72 0.999880 3.22 0.999994731.73 0.985578 2.23 0.998388 2.73 0.999887 3.23 0.999995071.74 0.986135 2.24 0.998464 2.74 0.999893 3.24 0.999995401.75 0.986672 2.25 0.998537 2.75 0.999899 3.25 0.999995701.76 0.987190 2.26 0.998607 2.76 0.999905 3.26 0.999995981.77 0.987691 2.27 0.998674 2.77 0.999910 3.27 0.999996241.78 0.988174 2.28 0.998738 2.78 0.999916 3.28 0.999996491.79 0.988641 2.29 0.998799 2.79 0.999920 3.29 0.999996721.80 0.989091 2.30 0.998857 2.80 0.999925 3.30 0.999996941.81 0.989525 2.31 0.998912 2.81 0.999929 3.31 0.999997151.82 0.989943 2.32 0.998966 2.82 0.999933 3.32 0.999997341.83 0.990347 2.33 0.999016 2.83 0.999937 3.33 0.999997511.84 0.990736 2.34 0.999065 2.84 0.999941 3.34 0.999997681.85 0.991111 2.35 0.999111 2.85 0.999944 3.35 0.9999978381.86 0.991472 2.36 0.999155 2.86 0.999948 3.36 0.9999979831.87 0.991821 2.37 0.999197 2.87 0.999951 3.37 0.9999981201.88 0.992156 2.38 0.999237 2.88 0.999954 3.38 0.9999982471.89 0.992479 2.39 0.999275 2.89 0.999956 3.39 0.9999983671.90 0.992790 2.40 0.999311 2.90 0.999959 3.40 0.9999984781.91 0.993090 2.41 0.999346 2.91 0.999961 3.41 0.9999985821.92 0.993378 2.42 0.999379 2.92 0.999964 3.42 0.9999986791.93 0.993656 2.43 0.999411 2.93 0.999966 3.43 0.9999987701.94 0.993923 2.44 0.999441 2.94 0.999968 3.44 0.9999988551.95 0.994179 2.45 0.999469 2.95 0.999970 3.45 0.9999989341.96 0.994426 2.46 0.999497 2.96 0.999972 3.46 0.9999990081.97 0.994664 2.47 0.999523 2.97 0.999973 3.47 0.9999990771.98 0.994892 2.48 0.999547 2.98 0.999975 3.48 0.9999991411.99 0.995111 2.49 0.999571 2.99 0.999977 3.49 0.9999992012.00 0.995322 2.50 0.999593 3.00 0.99997791 3.50 0.9999992572.01 0.995525 2.51 0.999614 3.01 0.99997926 3.51 0.9999993092.02 0.995719 2.52 0.999635 3.02 0.99998053 3.52 0.9999993582.03 0.995906 2.53 0.999654 3.03 0.99998173 3.53 0.9999994032.04 0.996086 2.54 0.999672 3.04 0.99998286 3.54 0.9999994452.05 0.996258 2.55 0.999689 3.05 0.99998392 3.55 0.9999994852.06 0.996423 2.56 0.999706 3.06 0.99998492 3.56 0.9999995212.07 0.996582 2.57 0.999722 3.07 0.99998586 3.57 0.9999995552.08 0.996734 2.58 0.999736 3.08 0.99998674 3.58 0.9999995872.09 0.996880 2.59 0.999751 3.09 0.99998757 3.59 0.999999617

- 18 -

x erf x x erf x x erf x x erf x3.60 0.999999644 3.70 0.999999833 3.80 0.999999923 3.90 0.9999999653.61 0.999999670 3.71 0.999999845 3.81 0.999999929 3.91 0.9999999683.62 0.999999694 3.72 0.999999857 3.82 0.999999934 3.92 0.9999999703.63 0.999999716 3.73 0.999999867 3.83 0.999999939 3.93 0.9999999733.64 0.999999736 3.74 0.999999877 3.84 0.999999944 3.94 0.9999999753.65 0.999999756 3.75 0.999999886 3.85 0.999999948 3.95 0.9999999773.66 0.999999773 3.76 0.999999895 3.86 0.999999952 3.96 0.9999999793.67 0.999999790 3.77 0.999999903 3.87 0.999999956 3.97 0.9999999803.68 0.999999805 3.78 0.999999910 3.88 0.999999959 3.98 0.9999999823.69 0.999999820 3.79 0.999999917 3.89 0.999999962 3.99 0.999999983

For x equal to, or greater than, 4 the following approximation may normally be used:

erf(x) 1 ex2

pi xSome complementary error function values for large x are:x erfc x4.0 1. 59 1084.1 6. 89 1094.2 2. 93 1094.3 1. 22 1094.4 5. 01 10104.5 2. 01 10104.6 7. 92 10114.7 3. 06 10114.8 1. 16 10114.9 4. 30 1012

Please recall that before calculating erf (z) you may need to use this conversion formulae relating the voltage x and mean value m to thestandard deviation of the noise :

z =x m

2And the CD or error probability is then given by:

P(x) = Pe =12

[ 1 + / erf (z) ]

The +/ sign is used in front of the erf function depending on whether the CD is to be calculated for values less/greater than x.

pmg/seccy/PER/TEACHING/COMNOTES/handout2007

Complementary Error Function Tablex erfc(x) x erfc(x) x erfc(x) x erfc(x) x erfc(x) x erfc(x) x erfc(x)

0 1.000000 0.5 0.479500 1 0.157299 1.5 0.033895 2 0.004678 2.5 0.000407 3 0.00002209

0.01 0.988717 0.51 0.470756 1.01 0.153190 1.51 0.032723 2.01 0.004475 2.51 0.000386 3.01 0.00002074

0.02 0.977435 0.52 0.462101 1.02 0.149162 1.52 0.031587 2.02 0.004281 2.52 0.000365 3.02 0.00001947

0.03 0.966159 0.53 0.453536 1.03 0.145216 1.53 0.030484 2.03 0.004094 2.53 0.000346 3.03 0.00001827

0.04 0.954889 0.54 0.445061 1.04 0.141350 1.54 0.029414 2.04 0.003914 2.54 0.000328 3.04 0.00001714

0.05 0.943628 0.55 0.436677 1.05 0.137564 1.55 0.028377 2.05 0.003742 2.55 0.000311 3.05 0.00001608

0.06 0.932378 0.56 0.428384 1.06 0.133856 1.56 0.027372 2.06 0.003577 2.56 0.000294 3.06 0.00001508

0.07 0.921142 0.57 0.420184 1.07 0.130227 1.57 0.026397 2.07 0.003418 2.57 0.000278 3.07 0.00001414

0.08 0.909922 0.58 0.412077 1.08 0.126674 1.58 0.025453 2.08 0.003266 2.58 0.000264 3.08 0.00001326

0.09 0.898719 0.59 0.404064 1.09 0.123197 1.59 0.024538 2.09 0.003120 2.59 0.000249 3.09 0.00001243

0.1 0.887537 0.6 0.396144 1.1 0.119795 1.6 0.023652 2.1 0.002979 2.6 0.000236 3.1 0.00001165

0.11 0.876377 0.61 0.388319 1.11 0.116467 1.61 0.022793 2.11 0.002845 2.61 0.000223 3.11 0.00001092

0.12 0.865242 0.62 0.380589 1.12 0.113212 1.62 0.021962 2.12 0.002716 2.62 0.000211 3.12 0.00001023

0.13 0.854133 0.63 0.372954 1.13 0.110029 1.63 0.021157 2.13 0.002593 2.63 0.000200 3.13 0.00000958

0.14 0.843053 0.64 0.365414 1.14 0.106918 1.64 0.020378 2.14 0.002475 2.64 0.000189 3.14 0.00000897

0.15 0.832004 0.65 0.357971 1.15 0.103876 1.65 0.019624 2.15 0.002361 2.65 0.000178 3.15 0.00000840

0.16 0.820988 0.66 0.350623 1.16 0.100904 1.66 0.018895 2.16 0.002253 2.66 0.000169 3.16 0.00000786

0.17 0.810008 0.67 0.343372 1.17 0.098000 1.67 0.018190 2.17 0.002149 2.67 0.000159 3.17 0.00000736

0.18 0.799064 0.68 0.336218 1.18 0.095163 1.68 0.017507 2.18 0.002049 2.68 0.000151 3.18 0.00000689

0.19 0.788160 0.69 0.329160 1.19 0.092392 1.69 0.016847 2.19 0.001954 2.69 0.000142 3.19 0.00000644

0.2 0.777297 0.7 0.322199 1.2 0.089686 1.7 0.016210 2.2 0.001863 2.7 0.000134 3.2 0.00000603

0.21 0.766478 0.71 0.315335 1.21 0.087045 1.71 0.015593 2.21 0.001776 2.71 0.000127 3.21 0.00000564

0.22 0.755704 0.72 0.308567 1.22 0.084466 1.72 0.014997 2.22 0.001692 2.72 0.000120 3.22 0.00000527

0.23 0.744977 0.73 0.301896 1.23 0.081950 1.73 0.014422 2.23 0.001612 2.73 0.000113 3.23 0.00000493

0.24 0.734300 0.74 0.295322 1.24 0.079495 1.74 0.013865 2.24 0.001536 2.74 0.000107 3.24 0.00000460

0.25 0.723674 0.75 0.288845 1.25 0.077100 1.75 0.013328 2.25 0.001463 2.75 0.000101 3.25 0.00000430

0.26 0.713100 0.76 0.282463 1.26 0.074764 1.76 0.012810 2.26 0.001393 2.76 0.000095 3.26 0.00000402

0.27 0.702582 0.77 0.276179 1.27 0.072486 1.77 0.012309 2.27 0.001326 2.77 0.000090 3.27 0.00000376

0.28 0.692120 0.78 0.269990 1.28 0.070266 1.78 0.011826 2.28 0.001262 2.78 0.000084 3.28 0.00000351

0.29 0.681717 0.79 0.263897 1.29 0.068101 1.79 0.011359 2.29 0.001201 2.79 0.000080 3.29 0.00000328

0.3 0.671373 0.8 0.257899 1.3 0.065992 1.8 0.010909 2.3 0.001143 2.8 0.000075 3.3 0.00000306

0.31 0.661092 0.81 0.251997 1.31 0.063937 1.81 0.010475 2.31 0.001088 2.81 0.000071 3.31 0.00000285

0.32 0.650874 0.82 0.246189 1.32 0.061935 1.82 0.010057 2.32 0.001034 2.82 0.000067 3.32 0.00000266

0.33 0.640721 0.83 0.240476 1.33 0.059985 1.83 0.009653 2.33 0.000984 2.83 0.000063 3.33 0.00000249

0.34 0.630635 0.84 0.234857 1.34 0.058086 1.84 0.009264 2.34 0.000935 2.84 0.000059 3.34 0.00000232

0.35 0.620618 0.85 0.229332 1.35 0.056238 1.85 0.008889 2.35 0.000889 2.85 0.000056 3.35 0.00000216

0.36 0.610670 0.86 0.223900 1.36 0.054439 1.86 0.008528 2.36 0.000845 2.86 0.000052 3.36 0.00000202

0.37 0.600794 0.87 0.218560 1.37 0.052688 1.87 0.008179 2.37 0.000803 2.87 0.000049 3.37 0.00000188

0.38 0.590991 0.88 0.213313 1.38 0.050984 1.88 0.007844 2.38 0.000763 2.88 0.000046 3.38 0.00000175

0.39 0.581261 0.89 0.208157 1.39 0.049327 1.89 0.007521 2.39 0.000725 2.89 0.000044 3.39 0.00000163

0.4 0.571608 0.9 0.203092 1.4 0.047715 1.9 0.007210 2.4 0.000689 2.9 0.000041 3.4 0.00000152

0.41 0.562031 0.91 0.198117 1.41 0.046148 1.91 0.006910 2.41 0.000654 2.91 0.000039 3.41 0.00000142

0.42 0.552532 0.92 0.193232 1.42 0.044624 1.92 0.006622 2.42 0.000621 2.92 0.000036 3.42 0.00000132

0.43 0.543113 0.93 0.188437 1.43 0.043143 1.93 0.006344 2.43 0.000589 2.93 0.000034 3.43 0.00000123

0.44 0.533775 0.94 0.183729 1.44 0.041703 1.94 0.006077 2.44 0.000559 2.94 0.000032 3.44 0.00000115

0.45 0.524518 0.95 0.179109 1.45 0.040305 1.95 0.005821 2.45 0.000531 2.95 0.000030 3.45 0.00000107

0.46 0.515345 0.96 0.174576 1.46 0.038946 1.96 0.005574 2.46 0.000503 2.96 0.000028 3.46 0.00000099

0.47 0.506255 0.97 0.170130 1.47 0.037627 1.97 0.005336 2.47 0.000477 2.97 0.000027 3.47 0.00000092

0.48 0.497250 0.98 0.165769 1.48 0.036346 1.98 0.005108 2.48 0.000453 2.98 0.000025 3.48 0.00000086

0.49 0.488332 0.99 0.161492 1.49 0.035102 1.99 0.004889 2.49 0.000429 2.99 0.000024 3.49 0.00000080

E&CE 411, Spring 2009, Table of Q Function 1

Table 1: Values of Q(x) for 0 x 9x Q(x) x Q(x) x Q(x) x Q(x)

0.00 0.5 2.30 0.010724 4.55 2.6823106 6.80 5.23110120.05 0.48006 2.35 0.0093867 4.60 2.1125106 6.85 3.692510120.10 0.46017 2.40 0.0081975 4.65 1.6597106 6.90 2.600110120.15 0.44038 2.45 0.0071428 4.70 1.3008106 6.95 1.826410120.20 0.42074 2.50 0.0062097 4.75 1.0171106 7.00 1.279810120.25 0.40129 2.55 0.0053861 4.80 7.9333107 7.05 8.945910130.30 0.38209 2.60 0.0046612 4.85 6.1731107 7.10 6.237810130.35 0.36317 2.65 0.0040246 4.90 4.7918107 7.15 4.338910130.40 0.34458 2.70 0.003467 4.95 3.7107107 7.20 3.010610130.45 0.32636 2.75 0.0029798 5.00 2.8665107 7.25 2.083910130.50 0.30854 2.80 0.0025551 5.05 2.2091107 7.30 1.438810130.55 0.29116 2.85 0.002186 5.10 1.6983107 7.35 9.910310140.60 0.27425 2.90 0.0018658 5.15 1.3024107 7.40 6.809210140.65 0.25785 2.95 0.0015889 5.20 9.9644108 7.45 4.66710140.70 0.24196 3.00 0.0013499 5.25 7.605108 7.50 3.190910140.75 0.22663 3.05 0.0011442 5.30 5.7901108 7.55 2.176310140.80 0.21186 3.10 0.0009676 5.35 4.3977108 7.60 1.480710140.85 0.19766 3.15 0.00081635 5.40 3.332108 7.65 1.004910140.90 0.18406 3.20 0.00068714 5.45 2.5185108 7.70 6.803310150.95 0.17106 3.25 0.00057703 5.50 1.899108 7.75 4.594610151.00 0.15866 3.30 0.00048342 5.55 1.4283108 7.80 3.095410151.05 0.14686 3.35 0.00040406 5.60 1.0718108 7.85 2.080210151.10 0.13567 3.40 0.00033693 5.65 8.0224109 7.90 1.394510151.15 0.12507 3.45 0.00028029 5.70 5.9904109 7.95 9.325610161.20 0.11507 3.50 0.00023263 5.75 4.4622109 8.00 6.22110161.25 0.10565 3.55 0.00019262 5.80 3.3157109 8.05 4.139710161.30 0.0968 3.60 0.00015911 5.85 2.4579109 8.10 2.74810161.35 0.088508 3.65 0.00013112 5.90 1.8175109 8.15 1.819610161.40 0.080757 3.70 0.0001078 5.95 1.3407109 8.20 1.201910161.45 0.073529 3.75 8.8417105 6.00 9.86591010 8.25 7.919710171.50 0.066807 3.80 7.2348105 6.05 7.24231010 8.30 5.205610171.55 0.060571 3.85 5.9059105 6.10 5.30341010 8.35 3.413110171.60 0.054799 3.90 4.8096105 6.15 3.87411010 8.40 2.232410171.65 0.049471 3.95 3.9076105 6.20 2.82321010 8.45 1.456510171.70 0.044565 4.00 3.1671105 6.25 2.05231010 8.50 9.479510181.75 0.040059 4.05 2.5609105 6.30 1.48821010 8.55 6.154410181.80 0.03593 4.10 2.0658105 6.35 1.07661010 8.60 3.985810181.85 0.032157 4.15 1.6624105 6.40 7.76881011 8.65 2.57510181.90 0.028717 4.20 1.3346105 6.45 5.59251011 8.70 1.659410181.95 0.025588 4.25 1.0689105 6.50 4.0161011 8.75 1.066810182.00 0.02275 4.30 8.5399106 6.55 2.87691011 8.80 6.840810192.05 0.020182 4.35 6.8069106 6.60 2.05581011 8.85 4.37610192.10 0.017864 4.40 5.4125106 6.65 1.46551011 8.90 2.792310192.15 0.015778 4.45 4.2935106 6.70 1.04211011 8.95 1.777410192.20 0.013903 4.50 3.3977106 6.75 7.39231012 9.00 1.128610192.25 0.012224

Erlang B (Blocked Calls Cleared)

No. of Traffic (A) in erlangs for P =Trunks

(N) 0.1% 0.2% 0.5% 1% 1.2% 1.3% 1.5% 2% 3% 5% 7% 10% 15% 20% 30% 40% 50%

1 0.001 0.002 0.005 0.010 0.012 0.013 0.02 0.020 0.031 0.053 0.075 0.111 0.176 0.250 0.429 0.667 1.002 0.046 0.065 0.105 0.153 0.168 0.176 0.19 0.223 0.282 0.381 0.470 0.595 0.796 1.00 1.45 2.00 2.733 0.194 0.249 0.349 0.455 0.489 0.505 0.53 0.602 0.715 0.899 1.06 1.27 1.60 1.93 2.63 3.48 4.594 0.439 0.535 0.701 0.869 0.922 0.946 0.99 1.09 1.26 1.52 1.75 2.05 2.50 2.95 3.89 5.02 6.505 0.762 0.900 1.13 1.36 1.43 1.46 1.52 1.66 1.88 2.22 2.50 2.88 3.45 4.01 5.19 6.60 8.44

6 1.15 1.33 1.62 1.91 2.00 2.04 2.11 2.28 2.54 2.96 3.30 3.76 4.44 5.11 6.51 8.19 10.47 1.58 1.80 2.16 2.50 2.60 2.65 2.73 2.94 3.25 3.74 4.14 4.67 5.46 6.23 7.86 9.80 12.48 2.05 2.31 2.73 3.13 3.25 3.30 3.40 3.63 3.99 4.54 5.00 5.60 6.50 7.37 9.21 11.4 14.39 2.56 2.85 3.33 3.78 3.92 3.98 4.08 4.34 4.75 5.37 5.88 6.55 7.55 8.52 10.6 13.0 16.3

10 3.09 3.43 3.96 4.46 4.61 4.68 4.80 5.08 5.53 6.22 6.78 7.51 8.62 9.68 12.0 14.7 18.3

11 3.65 4.02 4.61 5.16 5.32 5.40 5.53 5.84 6.33 7.08 7.69 8.49 9.69 10.9 13.3 16.3 20.312 4.23 4.64 5.28 5.88 6.05 6.14 6.27 6.61 7.14 7.95 8.61 9.47 10.8 12.0 14.7 18.0 22.213 4.83 5.27 5.96 6.61 6.80 6.89 7.03 7.40 7.97 8.83 9.54 10.5 11.9 13.2 16.1 19.6 24.214 5.45 5.92 6.66 7.35 7.56 7.65 7.81 8.20 8.80 9.73 10.5 11.5 13.0 14.4 17.5 21.2 26.215 6.08 6.58 7.38 8.11 8.33 8.43 8.59 9.01 9.65 10.6 11.4 12.5 14.1 15.6 18.9 22.9 28.2

16 6.72 7.26 8.10 8.88 9.11 9.21 9.39 9.83 10.5 11.5 12.4 13.5 15.2 16.8 20.3 24.5 30.217 7.38 7.95 8.83 9.65 9.89 10.0 10.19 10.7 11.4 12.5 13.4 14.5 16.3 18.0 21.7 26.2 32.218 8.05 8.64 9.58 10.4 10.7 10.8 11.00 11.5 12.2 13.4 14.3 15.5 17.4 19.2 23.1 27.8 34.219 8.72 9.35 10.3 11.2 11.5 11.6 11.82 12.3 13.1 14.3 15.3 16.6 18.5 20.4 24.5 29.5 36.220 9.41 10.1 11.1 12.0 12.3 12.4 12.65 13.2 14.0 15.2 16.3 17.6 19.6 21.6 25.9 31.2 38.2

P

AN

Ax

N

x

x

N

!

!0

20 9.41 10.1 11.1 12.0 12.3 12.4 12.65 13.2 14.0 15.2 16.3 17.6 19.6 21.6 25.9 31.2 38.2

21 10.1 10.8 11.9 12.8 13.1 13.3 13.48 14.0 14.9 16.2 17.3 18.7 20.8 22.8 27.3 32.8 40.222 10.8 11.5 12.6 13.7 14.0 14.1 14.32 14.9 15.8 17.1 18.2 19.7 21.9 24.1 28.7 34.5 42.123 11.5 12.3 13.4 14.5 14.8 14.9 15.16 15.8 16.7 18.1 19.2 20.7 23.0 25.3 30.1 36.1 44.124 12.2 13.0 14.2 15.3 15.6 15.8 16.01 16.6 17.6 19.0 20.2 21.8 24.2 26.5 31.6 37.8 46.125 13.0 13.8 15.0 16.1 16.5 16.6 16.87 17.5 18.5 20.0 21.2 22.8 25.3 27.7 33.0 39.4 48.1

26 13.7 14.5 15.8 17.0 17.3 17.5 17.72 18.4 19.4 20.9 22.2 23.9 26.4 28.9 34.4 41.1 50.127 14.4 15.3 16.6 17.8 18.2 18.3 18.59 19.3 20.3 21.9 23.2 24.9 27.6 30.2 35.8 42.8 52.128 15.2 16.1 17.4 18.6 19.0 19.2 19.45 20.2 21.2 22.9 24.2 26.0 28.7 31.4 37.2 44.4 54.129 15.9 16.8 18.2 19.5 19.9 20.0 20.32 21.0 22.1 23.8 25.2 27.1 29.9 32.6 38.6 46.1 56.130 16.7 17.6 19.0 20.3 20.7 20.9 21.19 21.9 23.1 24.8 26.2 28.1 31.0 33.8 40.0 47.7 58.1

31 17.4 18.4 19.9 21.2 21.6 21.8 22.07 22.8 24.0 25.8 27.2 29.2 32.1 35.1 41.5 49.4 60.132 18.2 19.2 20.7 22.0 22.5 22.6 22.95 23.7 24.9 26.7 28.2 30.2 33.3 36.3 42.9 51.1 62.133 19.0 20.0 21.5 22.9 23.3 23.5 23.83 24.6 25.8 27.7 29.3 31.3 34.4 37.5 44.3 52.7 64.134 19.7 20.8 22.3 23.8 24.2 24.4 24.72 25.5 26.8 28.7 30.3 32.4 35.6 38.8 45.7 54.4 66.135 20.5 21.6 23.2 24.6 25.1 25.3 25.60 26.4 27.7 29.7 31.3 33.4 36.7 40.0 47.1 56.0 68.1

36 21.3 22.4 24.0 25.5 26.0 26.2 26.49 27.3 28.6 30.7 32.3 34.5 37.9 41.2 48.6 57.7 70.137 22.1 23.2 24.8 26.4 26.8 27.0 27.39 28.3 29.6 31.6 33.3 35.6 39.0 42.4 50.0 59.4 72.138 22.9 24.0 25.7 27.3 27.7 27.9 28.28 29.2 30.5 32.6 34.4 36.6 40.2 43.7 51.4 61.0 74.139 23.7 24.8 26.5 28.1 28.6 28.8 29.18 30.1 31.5 33.6 35.4 37.7 41.3 44.9 52.8 62.7 76.140 24.4 25.6 27.4 29.0 29.5 29.7 30.08 31.0 32.4 34.6 36.4 38.8 42.5 46.1 54.2 64.4 78.1

Erlang B (Blocked Calls Cleared)

No. of Traffic (A) in erlangs for P =Trunks

(N) 0.1% 0.2% 0.5% 1% 1.2% 1.3% 1.5% 2% 3% 5% 7% 10% 15% 20% 30% 40% 50%

P

AN

Ax

N

x

x

N

!

!0

41 25.2 26.4 28.2 29.9 30.4 30.6 30.98 31.9 33.4 35.6 37.4 39.9 43.6 47.4 55.7 66.0 80.142 26.0 27.2 29.1 30.8 31.3 31.5 31.88 32.8 34.3 36.6 38.4 40.9 44.8 48.6 57.1 67.7 82.143 26.8 28.1 29.9 31.7 32.2 32.4 32.79 33.8 35.3 37.6 39.5 42.0 45.9 49.9 58.5 69.3 84.144 27.6 28.9 30.8 32.5 33.1 33.3 33.69 34.7 36.2 38.6 40.5 43.1 47.1 51.1 59.9 71.0 86.145 28.4 29.7 31.7 33.4 34.0 34.2 34.60 35.6 37.2 39.6 41.5 44.2 48.2 52.3 61.3 72.7 88.1

46 29.3 30.5 32.5 34.3 34.9 35.1 35.51 36.5 38.1 40.5 42.6 45.2 49.4 53.6 62.8 74.3 90.147 30.1 31.4 33.4 35.2 35.8 36.0 36.42 37.5 39.1 41.5 43.6 46.3 50.6 54.8 64.2 76.0 92.148 30.9 32.2 34.2 36.1 36.7 36.9 37.34 38.4 40.0 42.5 44.6 47.4 51.7 56.0 65.6 77.7 94.149 31.7 33.0 35.1 37.0 37.6 37.8 38.25 39.3 41.0 43.5 45.7 48.5 52.9 57.3 67.0 79.3 96.150 32.5 33.9 36.0 37.9 38.5 38.7 39.17 40.3 41.9 44.5 46.7 49.6 54.0 58.5 68.5 81.0 98.1

51 33.3 34.7 36.9 38.8 39.4 39.6 40.08 41.2 42.9 45.5 47.7 50.6 55.2 59.7 69.9 82.7 100.152 34.2 35.6 37.7 39.7 40.3 40.6 41.00 42.1 43.9 46.5 48.8 51.7 56.3 61.0 71.3 84.3 102.153 35.0 36.4 38.6 40.6 41.2 41.5 41.92 43.1 44.8 47.5 49.8 52.8 57.5 62.2 72.7 86.0 104.154 35.8 37.2 39.5 41.5 42.1 42.4 42.84 44.0 45.8 48.5 50.8 53.9 58.7 63.5 74.2 87.6 106.155 36.6 38.1 40.4 42.4 43.0 43.3 43.77 44.9 46.7 49.5 51.9 55.0 59.8 64.7 75.6 89.3 108.1

56 37.5 38.9 41.2 43.3 43.9 44.2 44.69 45.9 47.7 50.5 52.9 56.1 61.0 65.9 77.0 91.0 110.157 38.3 39.8 42.1 44.2 44.8 45.1 45.62 46.8 48.7 51.5 53.9 57.1 62.1 67.2 78.4 92.6 112.158 39.1 40.6 43.0 45.1 45.8 46.1 46.54 47.8 49.6 52.6 55.0 58.2 63.3 68.4 79.8 94.3 114.159 40.0 41.5 43.9 46.0 46.7 47.0 47.47 48.7 50.6 53.6 56.0 59.3 64.5 69.7 81.3 96.0 116.160 40.8 42.4 44.8 46.9 47.6 47.9 48.40 49.6 51.6 54.6 57.1 60.4 65.6 70.9 82.7 97.6 118.160 40.8 42.4 44.8 46.9 47.6 47.9 48.40 49.6 51.6 54.6 57.1 60.4 65.6 70.9 82.7 97.6 118.1

61 41.6 43.2 45.6 47.9 48.5 48.8 49.33 50.6 52.5 55.6 58.1 61.5 66.8 72.1 84.1 99.3 120.162 42.5 44.1 46.5 48.8 49.4 49.7 50.26 51.5 53.5 56.6 59.1 62.6 68.0 73.4 85.5 101.0 122.163 43.3 44.9 47.4 49.7 50.4 50.7 51.19 52.5 54.5 \\ 60.2 63.7 69.1 74.6 87.0 102.6 124.164 44.2 45.8 48.3 50.6 51.3 51.6 52.12 53.4 55.4 58.6 61.2 64.8 70.3 75.9 88.4 104.3 126.165 45.0 46.6 49.2 51.5 52.2 52.5 53.05 54.4 56.4 59.6 62.3 65.8 71.4 77.1 89.8 106.0 128.1

66 45.8 47.5 50.1 52.4 53.1 53.5 53.99 55.3 57.4 60.6 63.3 66.9 72.6 78.3 91.2 107.6 130.167 46.7 48.4 51.0 53.4 54.1 54.4 54.92 56.3 58.4 61.6 64.4 68.0 73.8 79.6 92.7 109.3 132.168 47.5 49.2 51.9 54.3 55.0 55.3 55.86 57.2 59.3 62.6 65.4 69.1 74.9 80.8 94.1 111.0 134.169 48.4 50.1 52.8 55.2 55.9 56.2 56.79 58.2 60.3 63.7 66.4 70.2 76.1 82.1 95.5 112.6 136.170 49.2 51.0 53.7 56.1 56.8 57.2 57.73 59.1 61.3 64.7 67.5 71.3 77.3 83.3 96.9 114.3 138.1

71 50.1 51.8 54.6 57.0 57.8 58.1 58.67 60.1 62.3 65.7 68.5 72.4 78.4 84.6 98.4 115.9 140.172 50.9 52.7 55.5 58.0 58.7 59.0 59.61 61.0 63.2 66.7 69.6 73.5 79.6 85.8 99.8 117.6 142.173 51.8 53.6 56.4 58.9 59.6 60.0 60.55 62.0 64.2 67.7 70.6 74.6 80.8 87.0 101.2 119.3 144.174 52.7 54.5 57.3 59.8 60.6 60.9 61.49 62.9 65.2 68.7 71.7 75.6 81.9 88.3 102.7 120.9 146.175 53.5 55.3 58.2 60.7 61.5 61.8 62.43 63.9 66.2 69.7 72.7 76.7 83.1 89.5 104.1 122.6 148.0

76 54.4 56.2 59.1 61.7 62.4 62.8 63.37 64.9 67.2 70.8 73.8 77.8 84.2 90.8 105.5 124.3 150.077 55.2 57.1 60.0 62.6 63.4 63.7 64.32 65.8 68.1 71.8 74.8 78.9 85.4 92.0 106.9 125.9 152.078 56.1 58.0 60.9 63.5 64.3 64.7 65.26 66.8 69.1 72.8 75.9 80.0 86.6 93.3 108.4 127.6 154.079 56.9 58.8 61.8 64.4 65.2 65.6 66.20 67.7 70.1 73.8 76.9 81.1 87.7 94.5 109.8 129.3 156.080 57.8 59.7 62.7 65.4 66.2 66.5 67.15 68.7 71.1 74.8 78.0 82.2 88.9 95.7 111.2 130.9 158.0

Erlang B (Blocked Calls Cleared)

No. of Traffic (A) in erlangs for P =Trunks

(N) 0.1% 0.2% 0.5% 1% 1.2% 1.3% 1.5% 2% 3% 5% 7% 10% 15% 20% 30% 40% 50%

P

AN

Ax

N

x

x

N

!

!0

81 58.7 60.6 63.6 66.3 67.1 67.5 68.09 69.6 72.1 75.8 79.0 83.3 90.1 97.0 112.6 132.6 160.082 59.5 61.5 64.5 67.2 68.0 68.4 69.04 70.6 73.0 76.9 80.1 84.4 91.2 98.2 114.1 134.3 162.083 60.4 62.4 65.4 68.2 69.0 69.4 69.99 71.6 74.0 77.9 81.1 85.5 92.4 99.5 115.5 135.9 164.084 61.3 63.2 66.3 69.1 69.9 70.3 70.93 72.5 75.0 78.9 82.2 86.6 93.6 100.7 116.9 137.6 166.085 62.1 64.1 67.2 70.0 70.9 71.2 71.88 73.5 76.0 79.9 83.2 87.7 94.7 102.0 118.3 139.3 168.0

86 63.0 65.0 68.1 70.9 71.8 72.2 72.83 74.5 77.0 80.9 84.3 88.8 95.9 103.2 119.8 140.9 170.087 63.9 65.9 69.0 71.9 72.7 73.1 73.78 75.4 78.0 82.0 85.3 89.9 97.1 104.5 121.2 142.6 172.088 64.7 66.8 69.9 72.8 73.7 74.1 74.73 76.4 78.9 83.0 86.4 91.0 98.2 105.7 122.6 144.3 174.089 65.6 67.7 70.8 73.7 74.6 75.0 75.68 77.3 79.9 84.0 87.4 92.1 99.4 106.9 124.0 145.9 176.090 66.5 68.6 71.8 74.7 75.6 76.0 76.63 78.3 80.9 85.0 88.5 93.1 100.6 108.2 125.5 147.6 178.0

91 67.4 69.4 72.7 75.6 76.5 76.9 77.58 79.3 81.9 86.0 89.5 94.2 101.7 109.4 126.9 149.3 180.092 68.2 70.3 73.6 76.6 77.4 77.8 78.53 80.2 82.9 87.1 90.6 95.3 102.9 110.7 128.3 150.9 182.093 69.1 71.2 74.5 77.5 78.4 78.8 79.48 81.2 83.9 88.1 91.6 96.4 104.1 111.9 129.7 152.6 184.094 70.0 72.1 75.4 78.4 79.3 79.7 80.43 82.2 84.9 89.1 92.7 97.5 105.3 113.2 131.2 154.3 186.095 70.9 73.0 76.3 79.4 80.3 80.7 81.39 83.1 85.8 90.1 93.7 98.6 106.4 114.4 132.6 155.9 188.0

96 71.7 73.9 77.2 80.3 81.2 81.6 82.34 84.1 86.8 91.1 94.8 99.7 107.6 115.7 134.0 157.6 190.097 72.6 74.8 78.2 81.2 82.2 82.6 83.29 85.1 87.8 92.2 95.8 100.8 108.8 116.9 135.5 159.3 192.098 73.5 75.7 79.1 82.2 83.1 83.5 84.25 86.0 88.8 93.2 96.9 101.9 109.9 118.2 136.9 160.9 194.099 74.4 76.6 80.0 83.1 84.1 84.5 85.20 87.0 89.8 94.2 97.9 103.0 111.1 119.4 138.3 162.6 196.0100 75.2 77.5 80.9 84.1 85.0 85.4 86.16 88.0 90.8 95.2 99.0 104.1 112.3 120.6 139.7 164.3 198.0100 75.2 77.5 80.9 84.1 85.0 85.4 86.16 88.0 90.8 95.2 99.0 104.1 112.3 120.6 139.7 164.3 198.0

101 76.1 78.4 81.8 85.0 86.0 86.4 87.12 88.9 91.8 96.3 100.0 105.2 113.4 121.9 141.2 165.9 200.0102 77.0 79.3 82.7 85.9 86.9 87.3 88.07 89.9 92.8 97.3 101.1 106.3 114.6 123.1 142.6 167.6 202.0103 77.9 80.2 83.7 86.9 87.8 88.3 89.03 90.9 93.8 98.3 102.2 107.4 115.8 124.4 144.0 169.2 204.0104 78.8 81.1 84.6 87.8 88.8 89.2 89.99 91.9 94.8 99.3 103.2 108.5 116.9 125.6 145.4 170.9 206.0105 79.6 82.0 85.5 88.8 89.7 90.2 90.94 92.8 95.7 100.4 104.3 109.6 118.1 126.9 146.9 172.6 208.0

106 80.5 82.8 86.4 89.7 90.7 91.1 91.90 93.8 96.7 101.4 105.3 110.7 119.3 128.1 148.3 174.2 210.0107 81.4 83.7 87.4 90.7 91.6 92.1 92.86 94.8 97.7 102.4 106.4 111.8 120.4 129.4 149.7 175.9 212.0108 82.3 84.6 88.3 91.6 92.6 93.1 93.82 95.7 98.7 103.4 107.4 112.9 121.6 130.6 151.1 177.6 214.0109 83.2 85.5 89.2 92.5 93.5 94.0 94.78 96.7 99.7 104.5 108.5 114.0 122.8 131.9 152.6 179.2 216.0110 84.1 86.4 90.1 93.5 94.5 95.0 95.74 97.7 100.7 105.5 109.5 115.1 124.0 133.1 154.0 180.9 218.0

111 85.0 87.3 91.0 94.4 95.5 95.9 96.70 98.7 101.7 106.5 110.6 116.2 125.1 134.3 155.4 182.6 220.0112 85.8 88.3 92.0 95.4 96.4 96.9 97.66 99.6 102.7 107.5 111.7 117.3 126.3 135.6 156.9 184.2 222.0113 86.7 89.2 92.9 96.3 97.4 97.8 98.62 100.6 103.7 108.6 112.7 118.4 127.5 136.8 158.3 185.9 224.0114 87.6 90.1 93.8 97.3 98.3 98.8 99.58 101.6 104.7 109.6 113.8 119.5 128.6 138.1 159.7 187.6 226.0115 88.5 91.0 94.7 98.2 99.3 99.7 100.54 102.5 105.7 110.6 114.8 120.6 129.8 139.3 161.1 189.2 228.0

116 89.4 91.9 95.7 99.2 100.2 100.7 101.50 103.5 106.7 111.7 115.9 121.7 131.0 140.6 162.6 190.9 230.0117 90.3 92.8 96.6 100.1 101.2 101.7 102.46 104.5 107.7 112.7 116.9 122.8 132.1 141.8 164.0 192.6 232.0118 91.2 93.7 97.5 101.1 102.1 102.6 103.43 105.5 108.7 113.7 118.0 123.9 133.3 143.1 165.4 194.2 234.0119 92.1 94.6 98.5 102.0 103.1 103.6 104.39 106.4 109.7 114.7 119.1 125.0 134.5 144.3 166.8 195.9 236.0120 93.0 95.5 99.4 103.0 104.0 104.5 105.35 107.4 110.7 115.8 120.1 126.1 135.7 145.6 168.3 197.6 238.0

Erlang B (Blocked Calls Cleared)

No. of Traffic (A) in erlangs for P =Trunks

(N) 0.1% 0.2% 0.5% 1% 1.2% 1.3% 1.5% 2% 3% 5% 7% 10% 15% 20% 30% 40% 50%

P

AN

Ax

N

x

x

N

!

!0

121 93.9 96.4 100.3 103.9 105.0 105.5 106.31 108.4 111.6 116.8 121.2 127.2 136.8 146.8 169.7 199.2 240.0122 94.7 97.3 101.2 104.9 105.9 106.4 107.28 109.4 112.6 117.8 122.2 128.3 138.0 148.1 171.1 200.9 242.0123 95.6 98.2 102.2 105.8 106.9 107.4 108.24 110.3 113.6 118.9 123.3 129.4 139.2 149.3 172.6 202.6 244.0124 96.5 99.1 103.1 106.8 107.9 108.4 109.21 111.3 114.6 119.9 124.4 130.5 140.3 150.6 174.0 204.2 246.0125 97.4 100.0 104.0 107.7 108.8 109.3 110.17 112.3 115.6 120.9 125.4 131.6 141.5 151.8 175.4 205.9 248.0

126 98.3 100.9 105.0 108.7 109.8 110.3 111.14 113.3 116.6 121.9 126.5 132.7 142.7 153.0 176.8 207.6 250.0127 99.2 101.8 105.9 109.6 110.7 111.2 112.10 114.3 117.6 123.0 127.5 133.8 143.9 154.3 178.3 209.2 252.0128 100.1 102.8 106.8 110.6 111.7 112.2 113.07 115.2 118.6 124.0 128.6 134.9 145.0 155.5 179.7 210.9 254.0129 101.0 103.7 107.8 111.5 112.6 113.2 114.03 116.2 119.6 125.0 129.6 136.0 146.2 156.8 181.1 212.6 256.0130 101.9 104.6 108.7 112.5 113.6 114.1 115.00 117.2 120.6 126.1 130.7 137.1 147.4 158.0 182.5 214.2 258.0

131 102.8 105.5 109.6 113.4 114.6 115.1 115.96 118.2 121.6 127.1 131.8 138.2 148.5 159.3 184.0 215.9 260.0132 103.7 106.4 110.6 114.4 115.5 116.0 116.93 119.1 122.6 128.1 132.8 139.3 149.7 160.5 185.4 217.6 262.0133 104.6 107.3 111.5 115.3 116.5 117.0 117.90 120.1 123.6 129.2 133.9 140.4 150.9 161.8 186.8 219.2 264.0134 105.5 108.2 112.4 116.3 117.4 118.0 118.87 121.1 124.6 130.2 134.9 141.5 152.0 163.0 188.3 220.9 266.0135 106.4 109.1 113.3 117.2 118.4 118.9 119.83 122.1 125.6 131.2 136.0 142.6 153.2 164.3 189.7 222.6 268.0

136 107.3 110.0 114.3 118.2 119.4 119.9 120.80 123.1 126.6 132.2 137.1 143.7 154.4 165.5 191.1 224.2 270.0137 108.2 111.0 115.2 119.1 120.3 120.9 121.77 124.0 127.6 133.3 138.1 144.8 155.6 166.8 192.5 225.9 272.0138 109.1 111.9 116.2 120.1 121.3 121.8 122.74 125.0 128.6 134.3 139.2 145.9 156.7 168.0 194.0 227.6 274.0139 110.0 112.8 117.1 121.0 122.2 122.8 123.71 126.0 129.6 135.3 140.2 147.0 157.9 169.3 195.4 229.2 276.0140 110.9 113.7 118.0 122.0 123.2 123.7 124.67 127.0 130.6 136.4 141.3 148.1 159.1 170.5 196.8 230.9 278.0140 110.9 113.7 118.0 122.0 123.2 123.7 124.67 127.0 130.6 136.4 141.3 148.1 159.1 170.5 196.8 230.9 278.0

141 111.8 114.6 118.9 123.0 124.2 124.7 125.64 128.0 131.6 137.4 142.4 149.2 160.2 171.8 198.3 232.6 280.0142 112.7 115.5 120.0 123.9 125.1 125.7 126.66 129.0 132.6 138.5 143.5 150.3 161.4 173.0 199.7 234.2 282.0143 113.5 116.3 120.8 124.9 126.1 126.7 127.59 129.9 133.6 139.5 144.5 151.4 162.6 174.2 201.1 235.9 284.0144 114.4 117.2 121.8 125.9 127.1 127.6 128.52 130.9 134.6 140.5 145.5 152.5 163.8 175.5 202.5 237.6 286.0145 115.3 118.2 122.7 126.8 128.0 128.6 129.54 132.0 135.7 141.6 146.6 153.6 164.9 176.7 204.0 239.2 288.0

146 116.3 119.2 123.7 127.8 129.0 129.5 130.46 132.9 136.6 142.6 147.6 154.7 166.1 178.0 205.4 240.9 290.0147 117.2 120.1 124.6 128.7 129.9 130.5 131.44 133.9 137.6 143.6 148.8 155.8 167.3 179.2 206.8 242.6 292.0148 118.1 121.0 125.5 129.6 130.9 131.4 132.38 134.8 138.6 144.7 149.8 156.9 168.5 180.5 208.2 244.2 294.0149 119.0 121.9 126.4 130.6 131.8 132.5 133.40 135.8 139.6 145.7 150.8 158.0 169.6 181.7 209.7 245.9 296.0150 119.9 122.8 127.4 131.6 132.8 133.4 134.39 136.8 140.7 146.7 151.9 159.1 170.8 183.0 211.1 247.6 298.0

Erlang C Traffic Table

Maximum Offered Load Versus B and NB is in %

N/B 0.01 0.05 0.1 0.5 1.0 2 5 10 15 20 30 40

1 .0001 .0005 .0010 .0050 .0100 .0200 .0500 .1000 .1500 .2000 .3000 .40002 .0142 .0319 .0452 .1025 .1465 .2103 .3422 .5000 .6278 .7403 .9390 1.1173 .0860 .1490 .1894 .3339 .4291 .5545 .7876 1.040 1.231 1.393 1.667 1.9034 .2310 .3533 .4257 .6641 .8100 .9939 1.319 1.653 1.899 2.102 2.440 2.7255 .4428 .6289 .7342 1.065 1.259 1.497 1.905 2.313 2.607 2.847 3.241 3.569

6 .7110 .9616 1.099 1.519 1.758 2.047 2.532 3.007 3.344 3.617 4.062 4.4287 1.026 1.341 1.510 2.014 2.297 2.633 3.188 3.725 4.103 4.406 4.897 5.2988 1.382 1.758 1.958 2.543 2.866 3.246 3.869 4.463 4.878 5.210 5.744 6.1789 1.771 2.208 2.436 3.100 3.460 3.883 4.569 5.218 5.668 6.027 6.600 7.065

10 2.189 2.685 2.942 3.679 4.077 4.540 5.285 5.986 6.469 6.853 7.465 7.959

11 2.634 3.186 3.470 4.279 4.712 5.213 6.015 6.765 7.280 7.688 8.336 8.85712 3.100 3.708 4.018 4.896 5.363 5.901 6.758 7.554 8.099 8.530 9.212 9.76113 3.587 4.248 4.584 5.529 6.028 6.602 7.511 8.352 8.926 9.379 10.09 10.6714 4.092 4.805 5.166 6.175 6.705 7.313 8.273 9.158 9.760 10.23 10.98 11.5815 4.614 5.377 5.762 6.833 7.394 8.035 9.044 9.970 10.60 11.09 11.87 12.49

16 5.150 5.962 6.371 7.502 8.093 8.766 9.822 10.79 11.44 11.96 12.77 13.4117 5.699 6.560 6.991 8.182 8.801 9.505 10.61 11.61 12.29 12.83 13.66 14.3318 6.261 7.169 7.622 8.871 9.518 10.25 11.40 12.44 13.15 13.70 14.56 15.2519 6.835 7.788 8.263 9.568 10.24 11.01 12.20 13.28 14.01 14.58 15.47 16.1820 7.419 8.417 8.914 10.27 10.97 11.77 13.00 14.12 14.87 15.45 16.37 17.10

21 8.013 9.055 9.572 10.99 11.71 12.53 13.81 14.96 15.73 16.34 17.28 18.0322 8.616 9.702 10.24 11.70 12.46 13.30 14.62 15.81 16.60 17.22 18.19 18.9623 9.228 10.36 10.91 12.43 13.21 14.08 15.43 16.65 17.47 18.11 19.10 19.8924 9.848 11.02 11.59 13.16 13.96 14.86 16.25 17.51 18.35 19.00 20.02 20.8225 10.48 11.69 12.28 13.90 14.72 15.65 17.08 18.36 19.22 19.89 20.93 21.76

26 11.11 12.36 12.97 14.64 15.49 16.44 17.91 19.22 20.10 20.79 21.85 22.6927 11.75 13.04 13.67 15.38 16.26 17.23 18.74 20.08 20.98 21.68 22.77 23.6328 12.40 13.73 14.38 16.14 17.03 18.03 19.57 20.95 21.87 22.58 23.69 24.5729 13.05 14.42 15.09 16.89 17.81 18.83 20.41 21.82 22.75 23.48 24.61 25.5030 13.71 15.12 15.80 17.65 18.59 19.64 21.25 22.68 23.64 24.38 25.54 26.44

31 14.38 15.82 16.52 18.42 19.37 20.45 22.09 23.56 24.53 25.29 26.46 27.3832 15.05 16.53 17.25 19.18 20.16 21.26 22.93 24.43 25.42 26.19 27.39 28.3333 15.72 17.24 17.97 19.95 20.95 22.07 23.78 25.30 26.32 27.10 28.31 29.2734 16.40 17.95 18.71 20.73 21.75 22.89 24.63 26.18 27.21 28.01 29.24 30.2135 17.09 18.67 19.44 21.51 22.55 23.71 25.48 27.06 28.11 28.92 30.17 31.16

36 17.78 19.39 20.18 22.29 23.35 24.53 26.34 27.94 29.00 29.83 31.10 32.1037 18.47 20.12 20.92 23.07 24.15 25.36 27.19 28.82 29.90 30.74 32.03 33.0538 19.17 20.85 21.67 23.86 24.96 26.18 28.05 29.71 30.80 31.65 32.97 34.0039 19.87 21.59 22.42 24.65 25.77 27.01 28.91 30.59 31.71 32.57 33.90 34.9440 20.58 22.33 23.17 25.44 26.58 27.84 29.77 31.48 32.61 33.48 34.83 35.89

41 21.28 23.07 23.93 26.23 27.39 28.68 30.63 32.37 33.51 34.40 35.77 36.8442 22.00 23.81 24.69 27.03 28.21 29.51 31.50 33.26 34.42 35.32 36.70 37.7943 22.71 24.56 25.45 27.83 29.02 30.35 32.36 34.15 35.33 36.23 37.64 38.74

44 23.43 25.31 26.22 28.63 29.84 31.19 33.23 35.04 36.23 37.15 38.58 39.6945 24.15 26.06 26.98 29.44 30.67 32.03 34.10 35.93 37.14 38.07 39.51 40.64

46 24.88 26.82 27.75 30.24 31.49 32.87 34.97 36.83 38.05 39.00 40.45 41.5947 25.60 27.57 28.52 31.05 32.32 33.72 35.84 37.72 38.96 39.92 41.39 42.5448 26.34 28.33 29.30 31.86 33.14 34.56 36.72 38.62 39.87 40.84 42.33 43.5049 27.07 29.10 30.08 32.68 33.97 35.41 37.59 39.52 40.79 41.76 43.27 44.4550 27.80 29.86 30.86 33.49 34.80 36.26 38.47 40.42 41.70 4?,69 44.21 45.40

51 28.54 30.63 31.64 34.31 35.64 37.11 39.35 41.32 42.61 43.61 45.15 46.3652 29.28 31.40 32.42 35.12 36.47 37.97 40.23 42.22 43.53 44.54 46.10 47.3153 30.03 32.17 33.21 35.94 37.31 38.82 41.10 43.12 44.44 45.47 47.04 48.2754 30.77 32.95 33.99 36.76 38.15 39.67 41.99 44.02 45.36 46.39 47.98 49.2255 31.52 33.72 34.78 37.59 38.99 40.53 42.87 44.93 46.28 47.32 48.93 50.18

56 32.27 34.50 35.57 38.41 39.83 41.39 43.75 45.83 47.20 48.25 49.87 51.1357 33.03 35.28 36.37 39.24 40.67 42.25 44.64 46.74 48.12 49.18 50.82 52.0958 33.78 36.06 37.16 40.07 41.51 43.11 45.52 47.64 49.04 50.11 51.76 53.0559 34.54 36.85 37.96 40.90 42.36 43.97 46.41 48.55 49.96 51.04 52.71 54.0160 35.30 37.63 38.76 41.73 43.20 44.83 47.29 49.46 50.88 51.97 53.65 54.96

61 36.06 38.42 39.56 42.56 44.05 45.70 48.18 50.37 51.80 52.90 54.60 55.9262 36.82 39.21 40.36 43.39 44.90 46.56 49.07 51.27 52.72 53.83 55.55 56.8863 37.59 40.00 41.16 44.23 45.75 47.43 49.96 52.18 53.64 54.77 56.49 57.8464 38.35 40.80 41.97 45.06 46.60 48.30 50.85 53.10 54.57 55.70 57.44 58.8065 39.12 41.59 42.78 45.90 47.45 49.16 51.74 54.01 55.49 56.63 58.39 59.76

66 39.89 42.39 43.58 46.74 48.30 50.03 52.64 54.92 56.42 57.57 59.34 60.7267 40.66 43.18 44.39 47.58 49.16 50.90 53.53 55.83 57.34 58.50 60.29 61.6868 41.44 43.98 45.20 48.42 50.01 51.77 54.42 56.75 58.27 59.44 61.24 62.6469 42.21 44.78 46.02 49.26 50.87 52.65 55.32 57.66 59.20 60.37 62.19 63.6070 42.99 45.58 46.83 50.10 51.73 53.52 56.21 58.57 60.12 61.31 63.14 64.56

71 43.77 46.39 47.64 50.95 52.59 54.39 57.11 59.49 61.05 62.25 64.09 65.5272 44.55 47.19 48.46 51.79 53.45 55.27 58.01 60.41 61.98 63.18 65.04 66.4873 45.33 48.00 49.28 52.64 54.31 56.14 58.90 61.32 62.91 64.12 65.99 67.4474 46.11 48.81 50.10 53.49 55.17 57.02 59.80 62.24 63.84 65.06 66.94 68.4075 46.90 49.61 50.92 54.34 56.03 57.90 60.70 63.16 64.76 66.00 67.89 69.37

76 47.68 50.42 51.74 55.19 56.89 58.78 61.60 64.07 65.69 66.94 68.85 70.3377 48.47 51.23 52.56 56.04 57.76 59.65 62.50 64.99 66.63 67.88 69.80 71.2978 49.26 52.05 53.38 56.89 58.62 60.53 63.40 65.91 67.56 68.82 70.75 72.2579 50.05 52.86 54.21 57.74 59.49 61.41 64.30 66.83 68.49 69.76 71.70 73.2280 50.84 53.68 55.03 58.60 60.36 62.30 65.21 67.75 69.42 70.70 72.66 74.18

81 51.63 54.49 55.86 59.45 61.22 63.18 66.11 68.67 70.35 71.64 73.61 75.1482 52.43 55.31 56.69 60.30 62.09 64.06 67.01 69.59 71.28 72.58 74.57 76.1183 53.22 56.13 57.52 61.16 62.96 64.94 67.92 70.52 72.22 73.52 75.52 77.0784 54.02 56.95 58.35 62.02 63.83 65.83 68.82 71.44 73.15 74.46 76.47 78.0485 54.81 57.77 59.18 62.88 64.70 66.71 69.73 72.36 74.08 75.40 77.43 79.00

86 55.61 58.59 60.01 63.73 65.57 67.60 70.63 73.28 75.02 76.35 78.38 79.9787 56.41 59.41 60.84 64.59 66.45 68.48 71.54 74.21 75.95 77.29 79.34 80.9388 57.21 60.23 61.67 65.45 67.32 69.37 72.45 75.13 76.89 78.23 80.30 81.9089 58.02 61.06 62.51 66.32 68.19 70.26 73.35 76.06 77.82 79.18 81.25 82.8690 58.82 61.88 63.34 67.18 69.07 71.15 74.26 76.98 78.76 80.12 82.21 83.83

91 59.62 62.71 64.18 68.04 69.94 72.04 75.17 77.91 79.69 81.06 83.16 84.7992 60.43 63.54 65.02 68.90 70.82 72.92 76.08 78.83 80.63 82.01 84.12 85.7693 61.23 64.36 65.86 69.77 71.70 73.81 76.99 79.76 81.57 82.95 85.08 86.7394 62.04 65.19 66.70 70.63 72.57 74.71 77.90 80.69 82.50 83.90 86.03 87.6995 62.85 66.02 67.54 71.50 73.45 75.60 78.81 81.61 83.44 84.84 86.99 88.66

96 63.66 66.85 68.38 72.36 74.33 76.49 79.72 82.54 84.38 85.79 87.95 89.6297 64.47 67.69 69.22 73.23 75.21 77.38 80.63 83.47 85.32 86.74 88.91 90.5998 65.28 68.52 70.06 74.10 76.09 78.27 81.54 84.39 86.26 87.68 89.87 91.5699 66.09 69.35 70.90 74.97 76.97 79.17 82.46 85.32 87.20 88.63 90.82 92.53

100 66.91 70.19 71.75 75.84 77.85 80.06 83.37 86.25 88.13 89.58 91.78 93.49

N is the number of servers. The numerical column headings indicate blocking probability B in %. Table generated by Dan Dexter