TABLE OF RANDOM SAMPLING NUMBERS随机数字表

TABLE OF RANDOM SAMPLING NUMBERS随机数字表 August 22, 1966 M20-2 APPENDIX C TABLE OF RANDOM SAMPLING NUMBERS 1. PURPOSE a. "Simple random sampling" is the simplest of all the methods that yield probability samples. It is also the method that is basic to all others. The most complex sample designs used generally involve in the selection procedure some application of simple random sampling. b. The heart of any simple random sampling process is the means or procedure by which randomness of selection is achieved. The selection procedure must be such that all the individual items in the population, or in certain subgroups within the population, are given an equal and independent chance to be selected into the sample. The selection procedure should also insure that all possible samples of a given type and size have the same chance of being selected. One of the most effective and practical ways to insure equal and independent probabilities of selection is to use a table of random sampling numbers. c. A literal application of the principle of equal probability of selection may be either impractical or impossible in certain situations. An example is sampling from a work process. A work process is conceived to represent an infinite population of work units that would result if the process were to operate indefinitely under the same causal conditions. There is no way to assign probabilities of selection to the infinite number of work units that could in theory be produced, but which in fact are not in existence at any time sampling takes place. d. As a practical matter, those work units actually produced, including new production as the processing of workunits is completed, represent the only output available for sampling. The total available output is itself only a sample of the process, but it necessarily must constitute the "frame" from which any smaller samples of a process are drawn. If at each stage of sampling from a work process, each a available unit is given an equal chance to be included in the sample, the sample so drawn is regarded as essentially a simple random sample. A table of random numbers may often be effectively used to insure randomness in the selection of such sample work units or other elements of a sample. 2. DESIGN AND USE a. A table of random numbers is a compilation of single and multidigit integral numbers whose frequency and sequence of occurrence have been determined entirely by chance. Since the position that any digit occupies in such a table is a result of chance, any number formed by a combination of such digits, and any sequence, group, or list of such digits or numbers, obtained by any progression, systematic or random, in any direction from any arbitrary starting point, may be regarded as a random grouping or selection. If a series of digits or numbers are allowed to represent a collection of objects to each of which, for purposes of identification, one of the numbers has been assigned, any partial selection of such objects which is based on the selection of their corresponding numbers from a table of random numbers, may be regarded as a random selection of such objects. App.C-1 M20-2 August 22, 1966 APPENDIX C b. The objects can be any collection of like things, for example, processed work units, claims folders on file, file cabinets in an office, employees at a field station, or work days in a month. The only requirement is that all such objects or things from which a random selection is to be made have, or be assigned, individual identifying numbers. Claims folders, for example, represent classes of objects already identified by assigned numbers. Employees often may be identified by their social security numbers, or by position numbers, or they may simply be counted and assigned numbers accordingly. File cabinets in an office and workdays in a month are not likely to have been numbered in advance and may require arbitrary designation by number. c. The totality of objects or items in any group of number-identified items may be regarded, for certain purposes, as a statistical population. A selection of any part of that totality of items by means of a table of random numbers may be regarded as a random sample of such items. Since tables of random digits or numbers were developed primarily for sampling purposes, they are often called tables of "random sampling numbers." It is important, however, to note that such tables can be used to randomize almost any kind of selection or choice, whether or not the selection itself is, or may result in, a "sample" of any kind. d. For convenience and simplicity in use, published tables of random numbers usually appear in the form of separate columns of five-digit numbers. Both rows and columns may be consecutively numbered for easy reference. The number of digits required for the numbers that are to be used in any given application of the table depends in general upon the size of the larger group or "population" of items from which the selection is to be made. More specifically, it depends upon the number of digits in the highest number assigned to members of the group to be sampled. e. For example, if the group consists of 84 items, numbered from I through 84, random numbers of two digits will be required. If in a larger group the highest number assigned is 796, random numbers of three digits are required. If in a still larger group the highest number assigned is 6,945,702, then seven-digit random numbers are required; and so on. To obtain a two-digit, three-digit, seven-digit, or other size number from the table, combine adjacent digits as needed. f. It is also important to recognize that random sample selection procedures can be developed which do not involve use of a random number table. For example, M21-4, chapter 3, subchapter 11, contains a random procedure used by Adjudication Divisions to select claims folders for quality control and other review purposes. The selection procedure is, in effect, equivalent to use of a table of random numbers, and can be audited to assure that the procedure was followed in selecting claims folders for review. g. Several pages of random sampling numbers are included at the end of this appendix. These pages have been extracted from a larger "Table of 105,000 Random Decimal Digits" issued in 1949 by the Bureau of Transport Economics and Statistics of the Interstate Commerce Commission. The source table was subjected by its compilers to various tests of randomness. Such tests are commonly made, when tables of random digits are developed, to provide assurance that the digits in each column and in each row of the table are in truth in random order. Therefore, it makes no difference where in the table one begins or in which App. C -2 August 22, 1966 M20-2 APPENDIX C direction he then moves in selecting random numbers. The following paragraphs suggest different uses of this table to achieve randomness in the selection of individual items for a single sample, or in making other types of random selections. 3. SELECTING INDIVIDUAL MEMBERS OF A P0PULATI0N into A SIMPLE RANDOM SAMPLE a. To select individual members or units of a population into a sample, the population must be finite or "countable," since the individual units must either have or be assigned identifying numbers. "Countability" is also required of the work units representing the outflow of a process, or the units of completed work available for sampling. To use the table, first determine the number of digits that are required in the numbers to be selected from the table. As indicated earlier, the number of digits needed is the same as the number of digits in the highest number assigned to any population unit. For example, if the highest numbered unit in the population is "8679" then the random numbers used in the table will contain four digits. The usable numbers for sample selection will be 0001,0002, 0003, extending to and closing with 8677, 8678, and 8679. Numbers in the table larger than 8679 are not usable and are passed over. b. For example, assume that the population is 8679 items numbered consecutively. Assume further that the starting point in the table selected is the first four digits in line 101, column (1). Assume also that it has been decided in advance that the numbers to be used in drawing the sample will be consecutive numbers obtained by reading across the columns from left to right on each successive line in the table until a sample of the desired size has been accumulated. If the first four digits of each number in each five-digit column are used, the sample would consist of units identified as numbers 1328, 1683, 7415, 2467, 3666, 0077, 2287, 0217, 5160, 0727, 7651, 4596, 2122, and so on until the desired sample size is obtained. The numbers 9202 and 9727, in columns (4) and (13), as well as any other number larger than 8679 that may later be encountered, are not usable for this population and are therefore passed over. The sample thus selected may be regarded as a simple random sample. This is because it is obtained by a procedure which gives every unit in the population an equal and independent chance of being selected. 4. SELECTING A SYSTEMATIC RANDOM SAMPLE a. A systematic random sample is one in which sample units are selected at specified intervals. A "random start" is required as a basis for selecting the units for each sample. A table of random numbers provides an easy and objective method of selecting a "random start." b. For example, assume that a listing or a file of 50,000 units represents the population from which a systematic random sample of 400 units is desired. The sample size, 400, is 400/50,000 or 1/125 of the population. From the table, select at random a number between I and 125 to begin the sample. If the number selected from the table is "64," the sample would consist of every 125th unit on the listing or in the file, beginning with the 64th unit. Thus, if the units in the population are numbered consecutively, the 64th, 189th, 314th, 439th, 564th, etc., units would be drawn as the sample. 5. SELECTING TERMINAL DIGITS AT RANDOM App. C-3 M20-2 August 22, 1966 APPENDIX C a. Many "document" or "record" populations of interest in VA operations are filed in such a way that population units are most easily accessible in groups classified by "terminal digits." These are specified ending digits in the identifying number which previously had been assigned to each unit. Examples of records usually filed by terminal digits, are claims folders, R&E folders, principal guardianship folders, insurance records, etc. Some of these records are classified by "primary digits," the last two digits in the identifying number. Others are classified first by "primary" and then by "secondary" digits, the latter being the fourth and third digits from the end of the number. Some types of records or documents are physically filed by terminal digit; other types have been re-corded on tape in sequences or reels by order of terminal digit. b. Any one "primary-digit" group of files, as all cards or folders whose last two digits are, for example, "19," or "38," or "76," constitutes in effect a preselected systematic sample. Any one such group makes up approximately l% of the total cards or folders in the file. If all three of the above groups of terminal digits, or any other combination of three groups were combined, a systematic sample of about 3% would be obtained. Although all such samples are "systematic" samples, for many purposes they may be regarded as equivalent to simple random samples, and the "control limits" or other measures of sampling error for simple random samples may be applied to them. By combining several complete primary terminal-digit groups, or by systematic or random subsampling within one or more such groups, almost any desired sample size can be closely approximated. c. To avoid possible biases, particularly in repeated use of terminal digit samples, any selection of terminal digit groups should be purely-random in nature. Such selection can easily be made by means of the table of random numbers. Tendencies current in many areas to overuse certain primary-digit groups, as for example "00" and "01," can be avoided by consistent use of the table. d. As an example of how the table maybe used for selecting terminal-digit samples, assume that a field station has a certain population of about 31,000 records of a particular type filed by primary digits, and that the sample size needed for a given purpose is about 900. The sample size can be closely approximated by combining three primary-digit groups. To select such groups at random, draw from the table three 2-digit numbers between "00" and "99." Suppose the last two digits of column (2) in line 159 are chosen as the starting point, and it has been decided previously to use the first three pairs of digits reading downward from the starting point. Thus, the terminal-digit groups selected at random to comprise the total sample would be 03, 72, and 55. Ordinarily, such a sample may be treated as equivalent to a simple random sample of all such records at the field station. e. It is important that the entire range of records, from the lowest to the highest number, be represented in any sample selected from any terminal-digit group. Otherwise, serious biases may develop because of under representation of certain ages or types of records in the sample. For example, suppose in the illustration cited in the preceding paragraph that a smaller sample of 100 records is desired from the population of 31,000 records. The first terminal-digit group selected at random from the table, "03," would provide a larger sample size than desired of about 300 records. Therefore, the procedure described in paragraph 4 above, may be used to obtain a "random start" from the table as a basis for selecting every third record in the "O3," terminal-digit group to obtain the desired sample size of 100. This selection procedure provides for representing in the sample the entire range of records in the terminal-digit group. By contrast, if say the first 100 records or the last 100 records in the "03," terminal-digit group were selected, the sample could easily under represent certain ages or types of records. App.C-4 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 1 10480 15011 01536 02011 81647 91646 69179 14194 62590 36207 20969 99570 91291 90700 2 22368 46573 25595 85393 30995 89198 27982 53402 93965 34095 52666 19174 39615 99505 3 24130 48360 22527 97265 76393 64809 15179 24830 49340 32081 30680 19655 63348 58629 4 42167 93093 06243 61680 07856 16376 39440 53537 71341 57004 00849 74917 97758 16379 5 37570 39975 81837 16656 06121 91782 60468 81305 49684 60672 14110 06927 01263 54613 6 77921 06907 11008 42751 27756 53498 18602 70659 90655 15053 21916 81825 44394 42880 7 99562 72905 56420 69994 98872 31016 71194 18738 44013 48840 63213 21069 10634 12952 8 96301 91977 05463 07972 18876 20922 94595 56869 69014 60045 18425 84903 42508 32307 9 89579 14342 63661 10281 74553 18103 57740 84378 25331 12566 58678 44947 05585 56941 10 85475 36857 53342 53988 53060 59533 38867 62300 08158 17983 16439 11458 18593 64952 11 28918 69578 88231 33276 70997 79936 56865 05859 90106 31595 01547 85590 91610 78188 12 63553 40961 48235 03427 49626 69445 18663 72695 52180 20847 12234 90511 33703 90322 13 09429 93969 52636 92737 88974 33488 36320 17617 30015 08272 84115 27156 30613 74952 14 10365 61129 87529 85689 48237 52267 67689 93394 01511 26358 85104 20285 29975 89868 15 07119 97336 71048 08178 77233 13916 47564 81056 97735 85977 29372 74461 28551 90707 16 51085 12765 51821 51259 77452 16308 60756 92144 49442 53900 70960 63990 75601 40719 17 02368 21382 52404 60268 89368 19885 55322 44819 01188 65255 64835 44919 05944 55157 18 01011 54092 33362 94904 31273 04146 18594 29852 71585 85030 51132 01915 92747 64951 19 52162 53916 46369 58586 23216 14513 83149 98736 23495 64350 94738 17752 35156 35749 20 07056 97628 33787 09998 42698 06691 76988 13602 51851 46104 88916 19509 25625 58104 21 48663 91245 85828 14346 09172 30168 90229 04734 59193 22178 30421 61611 99904 32812 22 54164 58492 22421 74103 47070 25306 76468 26384 58151 06646 21524 15227 96909 44592 23 32639 32363 05597 24200 13363 38005 94342 28728 35806 06912 17012 64161 18296 22851 24 29334 27001 87637 87308 58731 00256 05834 15398 46557 41135 10367 07684 36188 18510 25 02488 33062 28834 08751 19731 92420 60952 61280 50001 67658 32586 86679 50720 94953 26 81525 72295 04839 96423 24878 82651 66566 14778 76797 14780 13300 87074 79666 95725 27 29676 20591 68086 26432 46901 20849 89768 81536 86645 12659 92259 57102 80428 25280 28 00742 57392 39064 66432 84673 40027 32832 61362 98947 96067 64760 64584 96096 98253 29 05366 04213 25669 26422 44407 44048 37937 63904 45766 66134 75470 66520 34693 90449 30 91921 24618 64117 94305 26766 25940 39972 22209 71500 64568 91402 42416 07844 69618 31 00582 04711 87917 77341 42206 35126 74087 99547 81817 42607 43808 76655 62028 76630 32 00725 69884 62797 56170 86324 88072 76222 36086 84637 93161 76038 65855 77919 88006 33 69011 65795 95876 55293 18988 27354 26575 08625 40801 59920 29841 80150 12777 48501 34 25976 57948 29888 88604 67917 48708 18912 82271 65424 69774 33611 54262 85963 03547 35 09763 83473 73577 12908 30883 18317 28290 35797 05998 41688 34952 37888 38917 88050 36 91567 42595 27958 30134 04024 86385 29880 99730 55536 84855 29080 09250 79656 73211 37 17955 56349 90999 49127 20044 59931 06115 20542 18059 02008 73708 83517 36103 42791 38 46503 18584 18845 49618 02304 51038 20655 58727 28168 15475 56942 53389 20562 87338 39 92157 89634 94824 78171 84610 82834 09922 25417 44137 48413 25555 21246 35509 20468 40 14577 62765 35605 81263 39667 47358 56873 56307 61607 49518 89656 20103 77490 18062 41 98427 07523 33662 64270 01638 92477 66969 98420 04880 45585 46565 04102 46880 45709 42 34914 63976 88720 83765 34476 17032 87589 40836 32427 70002 70663 88863 77775 69348 43 70060 28277 39475 46473 23219 53416 94970 25832 69975 94884 19661 72828 00102 66794 44 53976 54914 06990 67245 68350 82948 11398 42878 80287 88267 47363 46634 06541 97809 45 76072 29515 40980 07391 58745 25774 22987 80059 39911 96189 41151 14222 60697 59583 46 90725 52210 83974 29992 65831 38857 50490 83765 55657 14361 31720 57375 56228 41546 47 64364 64712 33339 31926 14883 24413 59744 92351 97473 89286 35931 04110 23726 51900 48 08962 88358 31662 25388 61642 34072 81249 35648 56891 69352 48373 45578 78547 81788 49 95012 68379 93526 70765 10592 04542 76463 54328 02349 17247 28865 14777 62730 92277 50 15664 10493 20492 30391 91132 21999 59516 81652 27195 48223 46751 22923 32261 85653 App. C-5 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 51 16408 81899 04153 53381 79401 21438 83035 92350 36693 31238 59649 91754 72772 02238 52 18629 81953 05520 91962 04739 13092 97662 24822 94730 06496 35090 04822 86774 98289 53 73115 35101 47498 87637 99016 71060 88824 71013 18735 20286 23153 72924 35165 43040 54 57491 16703 23167 49323 45021 33132 12544 41035 80780 45393 44812 12515 98931 91202 55 30405 83946 23792 14422 15059 45799 22716 19792 09983 74353 68668 30429 70735 25499 56 16631 35006 85900 98275 32388 52390 16815 69298 82732 38480 73817 32523 41961 44437 57 96773 20206 42559 78985 05300 22164 24369 54224 35083 19687 11052 91491 60383 19746 58 38935 64202 14349 82674 66523 44133 00697 35552 35970 19124 63318 29686 03387 59846 59 31624 76384 17403 53363 44167 64486 64758 75366 76554 31601 12614 33072 60332 92325 60 78919 19474 23632 27889 47914 02584 37680 20801 72152 39339 34806 08930 85001 87820 61 03931 33309 57047 74211 63445 17361 62825 39908 05607 91284 68833 25570 38818 46920 62 74426 33278 43972 10119 89917 15665 52872 73823 73144 88662 88970 74492 51805 99378 63 09066 00903 20795 95452 92648 45454 09552 88815 16553 51125 79375 97596 16296 66092 64 42238 12426 87025 14267 20979 04508 64535 31355 86064 29472 47689 05974 52468 16834 65 16153 08002 26504 41744 81959 65642 74240 56302 00033 67107 77510 70625 28725 34191 66 21457 40742 29820 96783 29400 21840 15035 34537 33310 06116 95240 15957 16578 06004 67 21581 57802 02050 89728 17937 37621 47075 42080 97403 48626 68995 43805 33386 21597 68 55612 78095 83197 33732 05810 24813 86902 60397 16489 03264 88525 42786 05269 92532 69 44657 66999 99324 51281 84463 60563 79312 93454 68876 25471 93911 25650 12682 73572 70 91340 84979 46949 81973 37949 61023 43997 15263 80644 43942 89203 71795 99533 50501 71 91227 21199 31935 27022 84067 05462 35216 14486 29891 68607 41867 14951 91696 85065 72 50001 38140 66321 19924 72163 09538 12151 06878 91903 18749 34405 56087 82790 70925 73 65390 05224 72958 28609 81406 39147 25549 48542 42627 45233 57202 94617 23772 07896 74 27504 96131 83944 41575 10573 08619 64482 73923 36152 05184 94142 25299 84387 34925 75 37169 94851 39117 89632 00959 16487 65536 49071 39782 17095 02330 75301 00275 48280 76 11508 70225 51111 38351 194444 66499 71945 05422 13442 78675 84081 66938 93654 59894 77 37449 30362 06694 54690 04052 53115 62757 95348 78662 11163 81651 50245 34971 52924 78 46515 70331 85922 38329 57015 15765 97161 17869 45349 61796 66345 81073 49106 79860 79 30986 81223 42416 58353 21432 30502 32305 86482 05174 07901 54339 58861 74818 46942 80 63798 34995 46583 09785 44160 78128 83991 42865 92520 83531 80377 35909 81250 54238 81 82486 84846 99254 67632 43218 50076 21361 64816 51202 88124 41870 52689 51875 83556 82 21885 32906 92431 09060 64297 51674 64126 62570 26123 05155 59194 52799 28225 85762 83 60336 98782 07408 53458 13564 59089 26445 29789 85205 41001 12535 12133 14645 23541 84 43937 46891 24010 25560 86355 33941 25786 54990 71899 15475 95434 98227 21824 19585 85 97656 63175 89303 16275 07100 92063 21942 18611 47348 20203 18534 03862 78095 50136 86 03299 01221 05418 38982 55758 92237 26759 86367 21216 98442 08303 56613 91511 75928 87 79626 06486 83574 17668 07785 76020 79924 25651 83325 88428 85076 72811 22717 50585 88 85636 68335 47539 03129 65651 11977 02510 261113 99457 68645 34327 15152 55230 93448 89 18039 14367 61337 06177 12143 46609 32989 74014 64708 00533 35398 58408 13261 47908 90 08362 15656 60627 36478 65648 16764 53412 09013 07832 41574 17639 02163 60859 75567 91 79556 29068 04142 16268 15387 12856 66227 38358 22478 73373 88732 09443 82558 05250 92 92608 82674 27072 32534 17075 27698 98204 63863 11951 34648 88022 56148 34925 57031 93 23982 25835 40055 67006 12293 02753 14827 23235 35071 99704 37543 11601 35503 85171 94 09915 96306 05908 97901 28395 14186 00821 80703 70426 75647 76310 88717 37890 40129 95 59037 33300 26695 62247 69927 76123 50842 43834 86654 70959 79725 93872 28117 19233 96 42488 78077 69882 61657 34136 79180 97526 43092 04098 73571 80799 76536 71255 64239 97 46764 86273 63003 93017 31204 36692 40202 35275 57306 55543 53203 16098 47625 88684 98 03237 45430 55417 63282 90816 17349 88298 90183 36600 78406 06216 95787 42579 90730 99 86591 81482 52667 61582 14972 90053 89534 76036 49199 43716 97548 04379 46370 28672 100 38534 01715 94964 87288 65680 43772 39560 12918 86537 62738 19636 51132 25739 56947 App. C-6 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 101 13284 16834 74151 92027 24670 36665 00770 22878 02179 51602 07270 76517 97275 45960 102 21224 00370 30420 03883 94648 89428 41583 17564 27395 63904 41548 49197 82277 24120 103 99052 47887 81085 64933 66279 80432 65793 83287 34142 13241 30590 97760 35848 91983 104 00199 50993 98603 38452 87890 94624 69721 57484 67501 77638 44331 11257 71131 11059 105 60578 06483 28733 37867 07936 98710 98539 27186 31237 80612 44488 97819 70401 95419 106 91240 18312 17441 01929 18163 69201 31211 54288 39296 37318 65724 90401 79017 62077 107 97458 14229 12063 59611 32249 90466 33216 19358 02591 54263 88449 01912 07436 50813 108 35249 38646 34475 72417 60514 69257 12489 51924 86871 92446 36607 11458 30440 52639 109 38980 46600 11759 11900 46743 27860 77940 39298 97838 95145 32378 68038 89351 37005 110 10750 52745 38749 87365 58959 53731 89295 59062 39404 13198 59960 70408 29812 83126 111 36247 27850 73958 20673 37800 63835 71051 84724 52492 22342 78071 17456 96104 18327 112 70994 66986 99744 72438 01174 42159 11392 20724 54322 36923 70009 23233 65438 59685 113 99638 94702 11463 18148 81386 80431 90628 52506 02016 85151 88598 47821 00265 82525 114 72055 15774 43857 99805 10419 76939 25993 03544 21560 83471 43989 90770 22965 44247 115 24038 65541 85788 55835 38835 59399 13790 35112 01324 39520 76210 22467 83275 32286 116 74976 14631 35908 28221 39470 91548 12854 30166 09073 75887 36782 00268 97121 57676 117 35553 71628 70189 26436 63407 91178 90348 55359 80392 41012 36270 77786 89578 21059 118 35676 12797 51434 82976 42010 26344 92920 92155 58807 54644 58581 95331 78629 73344 119 74815 67523 72985 23183 02446 63594 98924 20633 58842 85961 07648 70164 34994 67662 120 45246 88048 65173 50989 91060 89894 36036 32819 68559 99221 49475 50558 34698 71800 121 76509 47069 86378 41797 11910 49672 88575 97966 32466 10083 54728 81972 58975 30761 122 19689 90332 04315 21358 97248 11188 39062 63312 52496 07349 79178 33692 57352 72862 123 42751 35318 97513 61537 54955 08159 00337 80778 27507 95478 21252 12746 37554 97775 124 11946 22681 45045 13964 57517 59419 58045 44067 58716 58840 45557 96345 33271 53464 125 96518 48688 20994 11090 48396 57177 83867 86464 14342 21545 46717 72364 86954 55580 126 35726 58643 76869 84622 39098 36083 72505 92265 23107 60278 05822 46760 44294 07672 127 39737 42750 48968 70536 84864 64952 38404 94317 65402 13589 01055 79044 19308 83623 128 97025 66492 56177 04049 80312 48028 26408 43591 75528 65341 49044 95495 81256 53215 129 62815 08075 09788 56350 76787 51591 54509 49295 85830 59860 30883 89660 96142 18354 130 25578 22950 15227 83291 41737 79599 96191 71845 86899 70694 24290 04551 80092 82118 131 68763 69576 88991 49662 46704 63362 56625 00481 73323 91427 15264 06969 57048 54149 132 17900 00813 64361 60725 88974 61005 99709 30666 26451 11528 44323 34778 60342 60388 133 71944 60227 63551 71109 05624 43836 58254 26160 32116 63403 35404 57146 10909 07346 134 54684 93691 85132 64399 29182 44324 14491 55226 78793 34107 30374 48429 51376 09559 135 25946 27623 11258 65204 52832 50880 22273 05554 99521 73791 85744 29276 70326 60251 136 01353 39318 44961 44972 91766 90262 56073 06606 51826 18893 83448 31915 97764 75091 137 99083 88191 27662 99113 57174 35571 99884 13951 71057 53961 61448 74909 07322 80960 138 52021 45406 37945 75234 24327 86978 22644 87779 23753 99926 63898 54886 18051 96314 139 78755 47744 43776 83098 03225 14281 83637 55984 13300 52212 58781 14905 46502 04472 140 25282 69106 59180 16257 22810 43609 12224 25643 89884 31149 85423 32581 34374 70873 141 11959 94202 02743 86847 79725 51811 12998 76844 05320 54236 53891 70226 38632 84776 142 11644 13792 98190 01424 30078 28197 55583 05197 47714 68440 22016 79204 06862 94451 143 06307 97912 68110 59812 95448 43244 31262 88880 13040 16458 43813 89416 42482 33939 144 76285 75714 89585 99296 52640 46518 55486 90754 88932 19937 57119 23251 55619 23679 145 55322 07598 39600 60866 63007 20007 66819 84164 61131 81429 60676 42807 78286 29015 146 78017 90928 90220 92503 83375 26986 74399 30885 88567 29169 72816 53357 15428 86932 147 44768 43342 20696 26331 43140 69744 82928 24988 94237 46138 77426 39039 55596 12655 148 25100 19336 14605 86603 51680 97678 24261 02464 86563 74812 60069 71674 15478 47642 149 83612 46623 62876 85197 07824 91392 58317 37726 84628 42221 10268 20692 15699 29167 150 41347 81666 82961 60413 71020 83658 02418 33322 66036 98712 46795 16308 28413 05417 App. C-7 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 151 38128 51178 75096 13609 16110 73533 42564 59870 29399 67834 91055 89917 51096 89011 152 60950 00455 73254 96067 50717 13878 03216 78274 65863 37011 91283 33914 91303 49326 153 90524 17320 29832 96118 75792 25326 22940 24904 80503 38928 91374 55597 97567 38914 154 49897 18278 67160 39408 97056 43517 84426 59650 20247 19293 02019 14790 02852 05819 155 18494 99209 81060 19488 65596 59787 47939 91225 98768 43688 00438 05548 09443 82897 156 65373 72984 30171 37741 70203 94094 87261 30056 58124 70133 18936 02138 59372 09075 157 40653 12843 04213 70925 95360 55774 76439 61768 52817 81151 52188 31940 54273 49032 158 51638 22238 56344 44587 83231 50317 74541 07719 25472 41602 77318 15145 57515 07633 159 69742 99303 62578 83575 30337 07488 51941 84316 42067 49692 28616 21901 03013 73449 160 58012 74072 67488 74580 47992 69482 58624 17106 47538 13452 22620 24260 40155 74716 161 18348 19855 42887 08279 43206 47077 42637 45606 00011 20662 14642 49984 94509 56380 162 59614 09193 58064 29086 44385 45740 70752 05663 49081 26960 57454 99264 24142 74648 163 75688 28630 39210 52897 62748 72658 98059 67202 72789 01869 13496 14663 87645 89713 164 13941 77802 69101 70061 35460 34576 15412 81304 58757 35498 94830 75521 00603 97701 165 96656 86420 96475 86458 54463 96419 55417 41375 76886 19008 66877 35934 59801 00497 166 03363 82042 15942 14549 38324 87094 19065 67590 11087 68570 22591 65232 85915 91499 167 70366 08390 69155 25496 13240 57407 91407 49160 07379 34444 94567 66035 38918 65708 168 47870 36605 12927 16043 53257 93796 52721 73120 48025 76074 95605 67422 41646 14557 169 79504 77606 22761 30518 28373 73898 30550 76684 77366 32276 04690 61667 64798 66276 170 46967 74841 50923 15339 37755 98995 40162 89561 69199 42257 11647 47603 48779 97907 171 14558 50769 35444 59030 87516 48193 02945 00922 48189 04724 21263 20892 92955 90251 172 12440 25057 01132 38611 28135 68089 10954 10097 54243 06460 50856 65435 79377 53890 173 32293 29938 68653 10497 98919 46587 77701 99119 93165 67788 17638 23097 21468 36992 174 10640 21875 72462 77981 56550 55999 87310 69643 45124 00349 25748 00844 96831 30651 175 47615 23169 39571 56972 20628 21788 51736 33133 72696 32605 41569 76148 91544 21121 176 16948 11128 71624 72754 49084 96303 27830 45817 67867 18062 87453 17226 72904 71474 177 21258 61092 66634 70335 92448 17354 83432 49608 66520 06442 59664 20420 39201 69549 178 15072 48853 15178 30730 47481 48490 41436 25015 49932 20474 53821 51015 79841 32405 179 99154 57418 09858 65671 70655 71479 63520 31357 56968 06729 34465 70685 04184 25250 180 08759 61089 23706 32994 35426 36666 63988 98844 37533 08269 27021 45886 22835 78451 181 67323 57839 61114 62192 47547 58023 64630 34886 98777 75442 95592 06141 45096 73117 182 09255 13986 84834 20764 72206 89393 34548 93438 88730 61805 78955 18952 46436 58740 183 36304 74712 00374 10107 85061 69228 81969 92216 03568 39630 81869 52824 50937 27954 184 15884 67429 86612 47367 10242 44880 12060 44309 46629 55105 66793 93173 00480 13311 185 18745 32031 35303 08134 33925 03004 59929 95418 04917 57596 24878 61733 92834 64454 186 78934 40086 88292 65728 38300 42323 64068 98373 48971 09049 59943 36538 05976 82118 187 17626 02944 20910 57662 60161 38579 24580 90529 52303 50436 29401 57824 86039 81062 188 27117 61399 50967 41399 81636 16663 15634 79717 94696 59240 25543 97989 63306 90946 189 93995 18678 90012 63645 85701 85269 62263 68331 00389 72571 15210 20769 44686 96176 190 67392 89421 09623 80725 62620 84162 87368 29560 00519 84545 08004 24526 41252 14521 191 04910 12261 37566 80016 21245 69377 50420 85658 55263 68667 78770 04533 14513 18099 192 81453 20283 79929 59839 23875 13245 46808 74124 74703 35769 95588 21014 37078 39170 193 19480 75790 48539 83703 15537 48885 02861 86587 74539 65227 90799 58789 96257 02708 194 21456 13162 74608 81011 55512 07481 93551 72189 76261 91206 89941 15132 37738 59284 195 09406 20912 46189 76376 25538 87212 20748 12831 57166 35026 16817 79121 18929 40628 196 09866 07414 55977 16419 01101 69343 13305 94302 80703 57910 36933 57771 42546 03003 197 86541 24681 23421 13521 28000 94917 07423 57523 97234 63951 42876 46829 09781 58160 198 10414 96941 06205 72222 57167 83902 07460 69507 20600 08858 07685 44472 64220 27040 199 49942 06683 41479 58982 56288 42853 92196 20632 62045 78812 35895 51851 83534 10689 200 23995 68882 42291 23374 24299 27024 67460 94703 40937 16961 26053 78749 48704 21983 App. C-8 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 201 78994 36244 02673 25475 84953 61793 50243 63423 69309 80308 49977 18075 43227 08266 202 04909 58485 70686 93930 34880 73059 06823 80257 44193 08337 47655 75932 29209 41954 203 46582 73570 33004 51795 86477 46736 60460 70345 37322 19987 67143 41129 89514 46892 204 29242 89792 88634 60285 07190 07795 27011 85941 01852 43096 31173 43730 48505 17958 205 68104 81339 97090 20601 78940 20228 22803 96070 10251 62711 66200 74330 13820 18966 206 17516 02182 82504 19880 93747 80910 78260 25136 62018 62919 73801 57195 83457 70597 207 50711 94789 07171 02103 99057 98775 37997 18325 88281 61091 97889 79977 04544 72963 208 39449 52409 75095 77720 39729 03205 09313 43545 43786 70443 41350 73369 42405 80516 209 75629 82729 76916 72657 58992 32756 01154 84890 04107 17469 59346 68651 97433 89491 210 01020 55151 36132 51971 32155 60735 64857 35424 25257 93844 39928 52519 34368 02114 211 08337 89989 24260 08618 66798 25889 52860 57375 52815 43539 18072 44270 27309 56535 212 76829 47229 19706 30094 69430 92399 98749 22081 52564 90431 35208 40323 87505 10227 213 39708 30641 21267 56501 95182 72442 21445 17276 90344 33199 02522 97883 09515 65930 214 89836 55817 56747 75195 06818 83043 47403 58266 52630 75573 91088 41118 27195 40650 215 25903 61370 66081 54076 67442 52964 23823 02718 28786 06121 29680 55295 67086 57574 216 71345 03422 01015 68025 19703 77313 04555 83425 46763 95315 23150 15116 18017 42730 217 61454 92263 14647 08473 34124 10740 40839 05620 62418 73374 92577 06755 21856 56272 218 80376 08909 30470 40200 46558 61742 11643 92121 22294 26648 69676 46198 00331 85186 219 45144 54373 05505 90074 24783 86299 20900 15144 26506 53770 76431 23861 71208 80694 220 12191 88527 58852 51175 11534 87218 04876 85584 78465 82182 03412 13217 14313 70593 221 62936 59120 73957 35969 21598 47287 39394 08778 38036 30140 89117 32054 44603 61849 222 31588 96798 43688 12611 01714 77266 55079 24690 84716 77732 35363 85525 17015 56344 223 20787 96048 84726 17512 39450 43618 30629 24356 05294 34236 65299 36922 46995 65765 224 45603 00745 84635 43079 52724 14262 05750 89373 79088 38088 65082 92504 80545 03090 225 31606 64782 34027 56734 09365 20008 93559 78384 99219 61747 96111 86965 33233 29812 226 10452 33074 76718 99556 16026 00013 78411 95107 10786 44886 44612 06830 27848 87597 227 37016 64633 67301 50949 91298 74968 73631 57397 08632 04762 39328 34926 07403 60916 228 66725 97865 25409 37498 00816 99262 14471 10332 19035 21695 07540 96447 20743 92472 229 07380 74438 82120 17890 40963 55757 13492 68294 87170 49468 40164 13374 23021 17006 230 71621 57688 58256 47702 74724 89419 08025 68519 95188 54788 32999 34374 05780 17506 231 03466 13263 23917 20417 11315 52805 33072 07723 87876 75258 22709 99869 11609 46666 232 12692 32931 97387 34832 53775 91674 96549 37635 91118 31062 89441 31839 88614 78168 233 52192 30941 44998 17833 94563 23062 95725 38463 03665 49189 46359 37401 73407 61817 234 569691 72529 66063 73570 86860 68125 40436 31303 79330 59083 34862 00540 21734 75535 235 74952 43041 53869 15677 78598 43520 97521 83248 52173 17636 77106 01044 22990 74874 236 18752 43693 32867 53017 22661 39610 03796 02622 78267 24503 73518 76545 99088 08369 237 61691 04944 43111 28325 82319 65589 66048 98498 46941 81427 44447 70357 18864 15525 238 49197 63948 38947 60207 70667 39843 60607 15328 09528 17277 84278 04463 12188 35359 239 19436 87291 71684 74859 76501 93456 95714 92518 10683 75617 78841 25315 74041 71554 240 39143 64893 14606 13543 09621 68301 69817 52140 03976 48795 60266 99592 68334 18790 241 82244 67549 76491 09761 74494 91307 64222 66592 67270 38593 18094 95095 08649 25047 242 55847 56155 42878 23708 97999 40131 52360 90390 73108 40475 80487 07787 35238 50990 243 94095 95970 07826 25991 37584 56966 68623 83454 49461 97707 12479 25041 40565 18383 244 11751 69469 25521 44097 07511 88976 30122 67542 54825 03274 02765 67162 40312 76127 245 69902 08995 27821 11758 64989 61902 32121 28165 21326 97375 44801 66977 08232 06807 246 21850 25352 25556 92161 23592 43294 10479 37879 21825 11453 29584 70067 09471 16319 247 75850 46992 25165 55906 62339 88958 91717 15756 78817 35541 01177 06869 10543 57652 248 29648 22086 42581 85677 20251 390641 65786 80689 49066 14456 91681 69371 18292 39377 249 82740 28443 42734 25518 82827 35825 90288 32911 79666 52959 01475 83321 24991 80102 250 36842 42092 52075 83926 420875 71500 69216 01350 92846 84792 874455 06842 22422 77379 App. C-9 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 251 89429 26726 15563 94972 78739 04419 60523 31022 23728 37647 16476 11170 68376 56874 252 43427 25412 25587 21276 44426 17369 29010 45337 90245 92053 41447 14897 18753 68291 253 58575 81958 51846 02676 67781 95137 88430 78260 66962 31812 12759 06427 40337 50115 254 61888 71246 24246 23487 78639 92006 63846 92263 33212 26516 93662 72399 88244 33922 255 73891 47025 40937 71907 26827 98865 38882 25757 26662 91441 89357 87803 61521 80600 256 40938 73894 40854 15997 55293 95033 31736 75068 91314 75293 04895 39355 54837 57203 257 98053 43567 17292 86908 71364 06089 92394 73691 57883 09983 35643 79309 53449 95334 258 59774 29138 46993 39836 99596 59050 25419 04130 54632 17223 94604 22973 97731 99476 259 09765 07548 63043 59782 81449 13652 94420 74460 46707 94303 85523 95244 70995 10742 260 38991 64502 24770 29209 82909 66610 84418 66214 26001 78685 69117 72446 79783 22305 261 25622 27100 56128 62145 82388 45197 97609 83942 01120 71717 32858 58679 97165 02810 262 21864 74120 66231 82306 91784 33177 17681 18963 07216 49288 43185 62797 00735 27085 263 81171 75639 60863 49562 28846 81581 10249 23190 53440 32357 16472 99013 24328 93670 264 69874 52803 28544 51569 56090 44558 42095 92311 57915 13368 13719 15833 38744 56065 265 27848 51107 05761 02159 53911 01952 59273 32250 39647 29908 49075 23061 07795 95047 266 69407 69736 75375 31488 67528 84234 76462 13628 21286 13736 67478 45218 27867 93049 267 29418 03091 06364 13151 40663 43633 87954 69800 24773 62596 52476 60631 50503 94116 268 38222 31231 79415 44558 62490 26936 49682 16307 98535 44822 99574 58487 85020 68881 269 94720 83796 93251 03568 62484 29140 14152 37044 90398 92042 35099 31640 99753 44409 270 45275 16852 02284 41361 73733 61486 33189 08907 41159 08147 15472 33250 17361 79961 271 97260 09552 82626 42915 45847 87401 13339 53850 34931 00602 75307 99708 77863 04924 272 01990 65259 60684 78175 43825 45211 86287 78190 02431 66251 74970 50246 23975 80697 273 24633 42314 81192 50253 67516 59076 92006 65676 87343 89231 15760 73706 69426 01979 274 98071 52677 74920 74461 52266 26967 68284 31612 40335 28865 98949 64492 96905 29184 275 34101 79442 88403 48541 13010 16596 72001 38546 76305 22119 82668 84017 44111 40302 276 77186 93967 25918 66403 73837 73445 86663 15929 08237 05647 15785 70444 58670 95967 277 23114 05481 42335 51396 60823 22680 50459 05429 35227 92559 24136 13126 22099 52388 278 59988 49944 41038 99977 16348 41119 51548 19511 90148 65604 16147 63445 60525 10480 279 11852 42254 82304 05588 75165 20179 94198 25700 33473 59554 30974 69973 57629 38550 280 59992 87922 56299 01700 07003 97507 69260 53349 86947 27517 80159 01899 46890 53850 281 42116 86593 22828 41422 18176 03250 06079 85467 32052 56922 96804 51060 33157 83948 282 39663 61401 24171 42702 70588 53144 27087 05591 57759 51394 98873 45625 61069 78783 283 53542 72009 96296 68908 58657 87117 21483 28879 20480 57309 95552 09826 79928 17141 284 25996 76108 98476 36397 89457 19577 65877 04802 61938 25032 09190 74932 36925 82686 285 91106 26450 11451 50328 29084 32332 08635 25192 31337 20249 95073 93800 70022 99968 286 37133 88924 27845 13024 90687 23726 11212 30414 42185 49224 46560 80447 24334 74866 287 13982 25736 10087 16762 02564 27250 79316 83848 38684 20552 44402 85153 94526 41256 288 26663 36187 81688 25005 46677 75851 73938 73044 05132 61204 90384 90296 03182 36672 289 62572 08275 16313 24936 81680 53829 40412 01479 24241 58488 65341 93414 07135 43446 290 65925 95455 08383 24643 72962 08172 37824 87587 40698 34964 50166 74756 77033 41501 291 97978 74676 08942 48919 51592 71196 48534 16955 25759 95645 03148 10646 15660 86520 292 01914 42524 67820 47985 91773 10383 89514 07557 02084 16736 39198 69697 62485 61938 293 68565 44811 39238 70394 78555 33539 56310 40809 63204 14479 19635 97299 66947 58010 294 54370 31672 03893 32423 54092 69375 63308 08016 28407 98287 22874 57545 72695 01604 295 79954 89601 23881 46951 69084 33477 87968 15639 82409 34125 36864 52112 27102 87334 296 55479 01059 44229 56975 06785 80930 26443 44892 77561 51123 34495 31376 06238 15973 297 38114 70330 42157 86699 46212 74692 92603 91306 58558 57280 50639 20563 71370 81487 298 29766 83452 66202 02488 72704 97821 70614 53616 39050 30355 15340 97298 41793 35185 299 31771 70640 34779 41831 33456 53194 19602 74194 61154 51774 76822 73794 54182 45264 300 77322 87188 83577 99067 83235 48662 31503 54829 54723 13177 15387 26073 68915 88415 App. C-10 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 301 64670 10396 82981 58320 71478 08143 48294 42631 45464 58092 14187 12271 98179 87812 302 25771 02205 73984 28436 88192 11470 11775 67385 66360 59884 93873 29948 66302 82227 303 25771 13537 54984 89406 88326 33993 92324 13249 35271 60400 70762 08343 76456 90068 304 91224 22417 44820 26189 57541 87558 45835 28461 54835 92411 44369 47512 49508 02841 305 75179 64320 71523 67868 38883 09674 27645 76240 47587 01677 38342 85598 12482 30749 306 64654 91085 65818 03313 39273 46384 66677 14148 87552 38383 67435 21072 63866 74644 307 98059 81123 67832 04102 66188 78200 67466 46043 65406 22834 08620 17509 51424 52187 308 38765 63585 18810 95805 11414 58096 00295 82626 42683 44518 12209 83245 53771 95469 309 01921 03564 71754 10213 80383 13473 94128 62199 59411 46782 62871 51149 87416 40129 310 16211 93671 27704 66778 96307 06732 63750 04191 40003 51653 54228 14916 05361 08884 311 70832 86076 61527 56123 48514 53935 86784 42351 67586 07432 61499 01773 97463 58815 312 22332 94265 67627 85815 00394 75271 98385 53697 56378 50592 77441 88505 89791 16331 313 81333 45965 64171 84367 15052 37965 03122 81914 69381 70034 92563 61804 58326 97895 314 39333 47453 66174 04546 10594 64271 61026 39471 55981 18628 67943 35599 37209 34061 315 29195 20825 50878 80273 26285 90070 79586 12449 77293 36577 59192 03658 90056 83145 316 74420 64037 06960 52109 08821 60143 34485 19257 29417 72713 72326 41572 41553 46946 317 22763 16508 24866 13177 07464 51790 65802 95718 28560 11332 74272 59189 53167 13133 318 72919 54618 40616 33287 51274 78491 53604 66742 97777 64468 98224 45485 17257 31561 319 91285 42402 15922 90033 21555 31647 22288 75692 20592 84620 58679 24587 83517 55327 320 85431 19857 97246 46118 71222 82744 67892 77155 10785 00344 19641 98279 18716 13895 321 40778 12451 14921 51464 45331 75822 46859 66829 35803 27645 76095 41535 25508 53066 322 88903 46592 60637 65231 08778 86813 47819 19218 46837 89671 77661 08518 85216 62664 323 29830 24899 85457 19548 83355 52479 77801 01596 48890 56104 68733 40830 58611 59181 324 22832 47422 08073 10107 46772 92299 42975 86376 27869 52954 07900 75918 51398 87598 325 75159 14809 11930 83531 51239 86298 72661 63015 98804 98491 99565 42801 71816 84000 326 99390 08217 56276 09263 82685 30451 25742 41105 74711 42007 02082 93025 86641 28952 327 68622 80897 08902 10867 91379 30068 84289 45020 92459 03831 08531 63496 98230 42884 328 92393 95901 41179 72129 72502 91097 09488 84896 37720 68104 73817 67626 16221 63527 329 53122 66033 38229 51879 29925 45574 53938 72801 64067 76328 28941 43645 37181 95329 330 43251 11941 86631 93264 53433 70281 55000 24550 74751 32855 25399 95743 85393 20261 331 16613 24901 34866 75002 55163 68300 20070 36953 39378 71191 84510 47599 93608 24379 332 12010 60852 92603 70393 17989 95755 14672 58786 41996 02893 94163 36156 54203 94138 333 85528 97879 27814 08219 02908 71582 31439 00360 72264 87245 65903 42298 28061 81889 334 32590 55079 33556 83169 92087 77939 53792 78795 58159 86394 41749 91623 26973 81474 335 91934 30650 16449 15805 61551 38689 59179 85485 18537 70496 98694 19796 76804 03673 336 80614 10150 09389 61892 79477 14522 40270 45744 29582 29717 39590 10223 43049 78775 337 62398 12034 90764 52872 22285 50592 42505 80560 38213 18917 10015 03887 62589 15851 338 02222 46811 05145 67916 15184 02636 59078 57773 21259 86090 56705 65556 04487 95954 339 08690 31785 61664 61322 24149 21471 23328 03093 31266 14840 30703 01640 07874 16630 340 61187 73897 66168 12885 73191 89432 65414 41886 75911 35708 43208 59193 04727 31037 341 12324 61149 85643 64999 63738 46671 25408 69313 54455 04917 35047 09951 72776 84697 342 47635 42279 98620 70677 52386 50904 97403 03931 42090 28179 98028 47728 45696 74176 343 70965 00390 08878 75373 70276 71889 86953 37931 23286 20508 40100 22486 37323 35429 344 58764 15262 96814 54548 00042 19721 78869 85937 36639 29135 12633 67225 69588 74178 345 07429 05609 31207 50254 68389 07714 92268 64698 32823 60122 46213 05646 54742 98304 346 15665 28659 54952 53217 76898 88931 25786 55912 85269 29212 84976 08888 94332 58528 347 64208 53232 99459 43605 04553 48451 68154 49436 49891 65524 65133 55163 76765 26006 348 17952 73276 52567 48489 64264 24220 55498 97548 98437 26033 39026 17377 43519 27425 349 60531 43217 39999 38615 97195 76928 87688 99010 90189 12522 00675 01995 82781 95130 350 76692 39999 43254 68110 88053 88727 14187 98623 84225 78440 67082 37425 40559 16838 App. C-11 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 351 06433 80674 24520 18222 10610 05794 37515 48619 62866 33963 14045 79451 04934 45576 352 39298 47829 72648 37414 75755 04717 29899 78817 03509 78673 73181 29973 18664 04555 353 89884 59651 67533 68123 17730 95862 08034 19473 63971 37271 31445 49019 49405 46925 354 61512 32155 51906 61662 64130 16688 37275 51262 11569 08697 91120 64156 40365 74297 355 99653 47635 12506 88535 36553 23757 34209 55803 96275 26130 47949 14877 69594 83041 356 95913 11085 13772 76638 48423 25018 99041 77529 81360 18180 97421 55541 90275 18213 357 55864 44004 13122 44115 01601 50541 00147 77685 58788 33016 61173 93049 04694 43534 358 35334 82410 91601 40617 72876 33967 73830 15405 96554 88265 34537 38526 67924 40474 359 57729 88646 76487 11622 96297 24160 09903 14047 22917 60718 66487 46346 30949 03173 360 86648 89317 63677 70119 94739 25875 38829 68377 43918 77653 04127 69930 43283 35766 361 30574 06039 07967 32422 76791 39725 53711 93385 13421 67957 20384 58731 53396 59723 362 81307 13114 83580 79974 45929 85113 72268 09858 52104 32014 53115 03727 98624 84616 363 02410 96385 79007 54939 21410 86980 91772 93307 34116 49516 42148 57740 31198 70336 364 18969 87444 52233 62319 08598 09066 95288 04794 01534 92058 03157 91758 80611 45357 365 87863 80514 66860 62297 80198 19347 73234 86265 49096 97021 92882 61422 75890 86442 366 68397 10538 15438 62311 72844 60203 46412 65943 79232 45702 67055 39024 57383 44424 367 28529 45247 58729 10854 99058 18260 38765 90038 94209 04055 27393 61517 23002 96560 368 44285 09452 15867 70418 57012 72122 36634 97283 95943 78363 36498 40662 94188 18202 369 86229 22510 33571 23309 57040 29285 67870 21913 72958 75637 99936 58715 07943 23748 370 84842 05748 90894 61658 15001 94055 36308 41161 37341 81838 19389 80336 46346 91895 371 56970 10799 52098 04184 54967 72938 56834 23777 98392 31417 98547 92058 02277 50315 372 83125 58077 60490 44369 66130 72936 69848 59973 08144 61070 73094 27059 69181 55623 373 55503 21383 02464 26141 68779 66388 75242 82690 74099 77885 23813 10054 11900 44653 374 47019 06683 33203 29608 54553 25971 69573 83854 24715 48866 65745 31131 47636 45137 375 84828 61152 79526 29554 84580 37859 28504 61980 34997 41825 11623 07320 15003 56774 376 68921 31331 79227 05748 51276 57143 31926 99915 45821 97702 87125 44488 77613 56823 377 36458 28285 30424 98420 72925 40729 22337 48293 86847 43186 42951 37804 85129 28993 378 95752 96065 36847 87729 81679 59126 59437 33225 31280 41232 34750 91097 60752 69783 379 26768 02513 58454 56958 20575 76746 49878 06846 32828 24425 30249 78801 26977 92074 380 42613 72456 43636 58085 06766 60227 96414 32671 45587 79620 84831 38156 74211 82752 381 95457 12176 65482 25596 02678 54592 63607 82096 21913 75544 55222 89796 05694 91552 382 95276 67524 63564 95958 39750 64379 46059 51666 10433 10945 55306 78562 89630 41230 383 66954 51574 64776 92345 95110 59448 77249 54044 67942 24145 42294 27427 84875 37022 384 17457 44151 14113 62462 02798 54977 48349 66738 60184 75679 38120 17640 36242 99357 385 03704 23322 83214 59337 01695 60666 97410 55064 17427 89180 74018 44865 53197 74810 386 21538 16997 33210 60337 27976 70661 08250 69599 60264 84549 78007 88450 06488 72274 387 57178 16739 98310 70348 11317 71623 55510 64756 87759 92354 78694 63638 80939 98644 388 31048 40058 94953 55866 96283 46620 52087 80817 74533 68407 55862 32476 19326 95558 389 69799 83300 16498 80733 96422 58078 99643 39847 96884 84657 33697 39578 90197 80532 390 90595 65017 59231 17772 67831 33317 00520 90401 41700 95510 61166 33757 23279 85523 391 13570 34761 98939 78784 09977 29398 93896 78227 90110 81378 96659 37008 04050 04228 392 15340 88760 57477 13898 48431 72936 78160 87240 52716 87697 79433 16336 52862 69149 393 64079 07733 36512 56186 99098 48850 72527 08486 10951 26832 39763 02485 71688 90936 394 63491 84886 67118 62063 74958 20946 28147 39338 32169 03713 93510 61244 73774 01245 395 92003 76568 41034 28260 79708 00770 88643 21188 01850 69689 49426 49128 14660 14143 396 52360 46658 66511 04172 73085 11795 52594 13287 82531 04388 64693 11934 35051 68576 397 74622 12142 68355 65635 21828 39539 18988 53609 04001 19648 14053 49623 10840 31915 398 04157 50979 61343 64315 70836 82857 35335 87900 36194 31567 53506 34304 39910 79630 399 86003 60070 66241 32836 27573 11479 94114 81641 00496 36058 75899 46620 70024 88753 400 41268 80187 20351 09636 84668 42486 71303 19512 50277 71508 20116 79520 06269 74173 App. C-12 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 401 05073 90103 85167 53900 19720 41488 57476 39458 16621 69774 47953 35039 39283 21573 402 93320 80269 56684 39192 53220 74539 26393 00787 94490 23386 38454 33466 32159 77439 403 18806 70257 96424 13606 14356 76599 25390 63236 04513 16358 30540 10551 32498 18685 404 22253 45923 29815 18578 23316 30896 64771 11220 86218 75956 22399 36234 61644 80682 405 93640 45982 40011 74142 29106 45729 43406 21457 04301 39651 76025 73819 11462 97385 406 47630 45980 76619 57138 57492 00030 77897 76236 64990 35985 57748 11606 72081 18359 407 01781 55061 07455 47083 71870 90597 10151 59606 96919 31174 99872 15843 99173 79512 408 69694 45054 33587 03664 95007 31567 25334 26433 75002 67607 33135 07076 82984 82675 409 51236 05052 26503 94651 29874 73492 88941 08488 09418 08173 63380 82067 58143 64983 410 89445 51039 73837 26720 38650 47322 68474 95047 20404 41577 46865 39849 78735 99192 411 40867 96834 02162 41517 88937 26099 56047 49164 35127 64916 75451 79160 14014 00445 412 92946 56944 93407 05010 54896 33173 30548 23667 43171 47849 40449 91072 91092 17613 413 75898 02275 90768 31902 52114 36634 46803 97970 92216 55398 75320 70475 82931 20172 414 22729 21695 90824 80500 09332 54667 46696 38166 02005 24615 85613 25948 75389 25765 415 28733 62663 23644 16416 47135 39137 62190 31032 58702 03805 67252 23712 92697 19071 416 51323 37770 42114 79742 59905 38480 25293 32993 36946 62701 51198 72941 52215 85257 417 69325 65551 49927 68073 56979 49454 79451 60753 70872 07422 06399 75240 80847 78231 418 11333 60801 36992 76128 27959 41306 93543 15926 99159 27102 98684 80175 98732 45405 419 86347 03703 36778 72501 95229 65735 14269 50220 77270 68604 05677 23347 43686 31584 420 73452 36179 82893 92262 43850 31888 71151 40682 49775 63628 45415 96270 31735 01509 421 75483 74009 73699 05870 36804 89338 73891 40740 98753 74566 74733 34777 05786 38294 422 73302 84917 75122 34085 86208 98399 79433 61960 01720 87458 24023 89971 09532 68155 423 42785 24350 05933 65282 12832 75382 29826 33197 81781 53542 63985 57022 22712 61343 424 40429 33209 58622 09308 38098 55947 12001 73526 23170 13721 37856 85602 74299 01346 425 92876 58271 99325 12301 72957 22690 62705 73892 01974 77759 92733 11331 08323 86196 426 32951 39844 99126 94838 48715 36586 42076 15283 19280 29166 24522 73131 83401 38920 427 099772 28139 48130 73301 35915 90923 19255 75242 84655 30163 75510 83315 98529 93805 428 78459 91322 50072 77941 65046 78363 21951 42319 46472 67617 34134 05905 61251 51040 429 14419 96517 99075 43664 81119 63487 95589 51785 07398 23245 10086 40097 46173 00507 430 97769 50967 24427 21011 92226 44380 23422 10654 43617 80504 90663 60751 79728 41132 431 09175 37545 39088 06879 21277 05153 81855 84043 35307 59465 75395 74758 09427 84460 432 52062 95519 54087 14072 50953 63477 64635 34552 75243 70222 75023 81454 70606 31861 433 70558 85169 01086 97202 10390 01819 88167 21851 87837 85287 69883 08289 74968 46947 434 22553 61317 08968 67521 16627 48855 97263 94242 93354 72446 28840 88195 82751 94352 435 95216 75263 60351 02643 00063 20824 67468 89441 84055 47035 29741 47972 61914 66864 436 49087 61399 47781 32173 96672 04528 15881 46764 20115 03226 79308 31970 49804 85150 437 24808 79068 70787 43106 97133 37236 77888 48451 20788 44648 70350 54965 57715 94826 438 89879 79942 43781 05069 80143 59176 47392 70372 26899 16228 71205 14564 97087 95690 439 61178 79295 58926 21977 28435 32631 23062 31822 70462 05965 22312 33013 74612 23733 440 37444 56047 23208 34710 12147 28558 58817 98807 56776 08129 08794 23646 92846 61706 441 99633 00363 16853 20789 87674 03938 36077 41012 08813 51168 78822 37353 62181 31172 442 87363 59239 42023 78056 51254 95644 90527 41398 74996 94977 22149 96616 54435 52469 443 23923 87269 85277 34727 78036 74471 12157 11655 25194 47557 26181 67825 80224 41490 444 45610 26370 13094 34500 36750 54517 85011 26567 04021 32485 58903 43529 24191 91832 445 44166 80095 08286 38126 48834 73423 13617 08853 16286 16023 77901 39118 14288 39385 446 81876 27486 53925 22330 37168 97954 11967 03309 97096 64221 11318 98720 01100 13651 447 79400 83852 52174 42577 18553 14023 69629 61913 41050 69689 57284 38160 57756 16762 448 42799 46647 36718 49704 17150 07935 62372 39933 20838 27652 54801 41067 08240 35163 449 09302 36408 64569 93033 95645 56791 14830 81699 45057 85796 63756 93944 60649 84847 450 88078 81456 17242 84590 93660 34619 51965 85618 36558 54410 68456 98504 83011 19393 App. C-13 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 451 85018 23508 91507 76455 54941 72711 39406 94620 27963 96478 21559 19246 88097 44926 452 11904 73678 08272 62941 02349 71389 45605 60947 60775 73181 43264 56895 04232 59604 453 75344 98489 86268 73652 98210 44546 27174 27499 53523 63110 57106 20865 91683 80688 454 65566 65614 01443 07607 11826 91326 29664 01603 23156 89223 43429 95353 44662 59433 455 51872 72294 95432 53555 96810 17100 35066 00815 01552 06392 31437 70385 45863 75971 456 03805 37913 98633 81009 81060 33449 68055 83844 90942 74857 52419 68723 47830 63010 457 21055 78685 71250 10329 56135 80647 51404 06626 10042 93629 37609 57215 08409 81906 458 48977 36794 56054 59243 57361 65304 93258 56760 63348 24949 11839 29793 37457 59377 459 93077 72941 92779 23581 24548 56415 61927 64416 29934 00755 09418 14230 62887 92683 460 84533 26564 91583 83411 66504 02036 02922 63569 17906 38076 32135 19096 96970 75917 461 11338 12903 14514 27585 45068 05520 56321 22693 35089 07694 04252 23791 60249 83010 462 23858 68500 92274 87026 99717 01542 72990 43413 59744 44595 71326 91382 45114 20245 463 94096 74920 25822 98026 05394 61840 83089 09224 78530 33996 49965 04851 18280 14039 464 83160 82362 09350 98536 38155 42661 02363 67625 34683 95372 74733 63558 09665 22610 465 97425 47335 69709 01386 74319 04318 99387 86874 12549 38369 54952 91579 26023 81076 466 83951 11954 24317 20345 18134 90062 10761 54548 49505 52685 63903 13193 33905 66936 467 93085 35203 05740 03206 92012 42710 34650 73236 66167 21788 03581 40699 10396 81827 468 33762 83193 58045 89880 78101 44392 53767 15220 66319 72953 14071 59148 95154 72852 469 49665 85397 85137 30496 23469 42846 94810 16151 08029 50554 03891 38313 34016 18671 470 37541 82627 80051 72521 35342 56119 97190 43635 84249 61254 80993 55431 90793 62603 471 22145 85304 35348 82854 55846 18076 12415 30193 42776 85611 57635 51362 79907 77364 472 27153 08662 61078 52433 22184 33998 87436 37430 45246 11400 20986 43996 73122 88474 473 00301 49425 66682 25442 83668 66236 79655 88312 93047 12088 86937 70794 01041 74867 474 43815 43272 73778 63469 50083 70696 13558 98995 58159 04700 90443 13168 31553 67891 475 14689 86482 74157 46012 97765 27552 49617 51734 20849 70198 67906 00880 82899 66065 476 16680 55936 82453 19532 49988 13176 94219 88698 41755 56216 66852 17748 04963 54859 477 86938 60429 01137 86168 78257 86249 46134 51865 09836 73966 65711 41699 11732 17173 478 33944 29219 73161 46061 30946 22210 79302 40300 08852 27528 84648 79589 95295 72895 479 16045 67736 18608 18198 19468 76358 69203 02760 28625 70476 76410 32988 10194 94917 480 37044 52523 25627 63107 30806 80857 84383 78450 26245 91763 73117 33047 03577 62599 481 61471 45322 35340 35132 42163 69332 98851 50252 56911 62693 73817 98693 18728 94741 482 47422 21296 16785 66393 39249 51463 95963 07929 66728 47761 81472 44806 15592 71357 483 24133 39719 14484 58613 88717 29289 77360 09030 39605 87507 85446 51257 89555 75520 484 67253 67064 10748 16006 16767 57345 42285 56670 88445 85799 76200 21795 38894 58070 485 62382 76941 01635 35829 77516 98468 51686 48140 13583 94911 13318 64741 64336 95103 486 98011 16503 09201 03523 87192 66483 55649 36764 86132 12463 28385 94242 32063 45233 487 37366 24386 20654 85117 74078 64120 04643 14351 71381 28133 68269 65145 28152 39087 488 73587 83993 54176 05221 94119 20108 78101 81276 00835 63835 87174 42446 08882 27067 489 33583 68291 50547 96085 62180 27453 18567 55524 86088 00069 59254 24654 77371 26409 490 02878 33223 39199 49536 56199 05993 71201 78852 65889 32719 13758 23937 90740 16866 491 91498 41673 17195 33175 04994 09879 70337 11861 69032 51915 23510 32050 52052 24004 492 91127 19815 30219 55591 21725 43827 78862 67699 01009 07050 73324 06732 27510 33761 493 12997 55013 18662 81724 24305 37661 18956 50064 39500 17450 18030 63124 48061 59412 494 96098 13651 15393 69995 14762 69734 89150 93126 17700 94400 76075 08317 27324 72723 495 97627 17837 10472 18983 28387 99781 52977 01657 92602 41043 05686 15650 29970 95877 496 40064 47981 31484 76603 54088 91095 00010 13800 76690 75133 60456 28491 03845 11507 497 16239 68743 71374 55863 22672 91609 51514 98135 42870 48578 29036 69876 86563 61729 498 58354 24913 20435 30965 17453 65623 93058 08313 99293 00990 13595 77457 79969 11339 499 52567 65085 60220 84641 18273 49604 47418 90974 83965 62732 85161 54330 22406 86253 500 06236 29052 91392 07551 83532 68130 56970 33273 61993 88407 69399 17301 70975 99129 App. C-14 TABLE OF RANDOM SAMPLING NUMBERS Col./Line (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 501 88188 99345 94118 40373 50387 24802 81352 61640 56614 71506 75541 37818 88047 94144 502 05200 50533 59428 02797 16833 10038 18901 40743 99449 49825 44637 72724 42649 67052 503 82828 41316 92617 31346 89263 06589 07121 07151 23905 98435 50453 12983 04738 76421 504 71006 99318 19269 35233 79183 78538 06326 62715 28701 52809 56581 05925 85210 17745 505 05937 00875 32264 82808 00229 03868 71072 11519 44876 34508 07859 62424 54319 32842 506 06021 04370 93070 90737 05354 68427 25554 11165 00123 80338 03876 85648 24978 01687 507 54789 10960 44023 57857 56556 83993 70787 28193 65872 33723 00125 99818 85571 69509 508 90400 05707 29128 14859 84117 72206 53740 00464 51853 78852 83593 82926 48985 64355 509 51424 01651 99970 73521 82356 03297 36288 93531 69269 84798 78962 06336 95618 89718 510 79743 88757 43370 86536 07166 06401 14413 23643 21527 91902 91384 31444 54783 38760 511 77418 00322 98854 51507 00565 33066 65791 47857 32483 38493 52606 91078 13631 67863 512 17580 49302 16408 05678 75532 46218 74359 77556 82242 00134 70154 09027 79459 18730 513 15489 45559 28548 64330 42126 43145 81287 73884 69312 03395 06879 49662 40000 61598 514 56342 66773 18536 32600 73958 75993 84250 19254 06677 54192 53422 58200 74464 73949 515 20202 19216 23762 47856 04623 70728 86657 70801 53719 25214 65635 07565 49977 45525 516 84877 51708 69357 67914 55372 97225 52837 46723 00256 96221 26641 00309 36009 48392 517 01647 00311 44989 21900 96079 15793 13148 01433 78721 02647 25454 53913 97554 41578 518 45652 89311 45302 74539 32045 86727 40595 55953 93448 07805 53622 27330 18749 57867 519 79975 06153 08932 59185 71386 19070 87098 19392 13899 56096 83645 45871 35950 52272 520 49744 54713 37053 77467 15348 03383 96086 93295 12413 55774 97318 66402 11209 52495 521 40922 94903 29638 46870 14108 84391 87313 65969 43349 85142 25650 01896 48680 51236 522 53319 48020 77444 51447 07916 99506 83504 22290 63835 45589 04884 92760 70462 00538 523 76682 10559 85446 56236 85919 76388 59850 03262 60347 31077 07165 26588 31296 56112 524 48869 97229 69581 84581 71728 45150 16901 88717 62688 24822 89469 35483 76532 30256 525 95961 19279 38078 17473 43945 21562 90937 52140 73771 56084 08775 94820 78139 25987 526 16521 25945 94076 91281 92272 41233 58614 18912 58454 34011 85969 83621 92099 19131 527 78282 26332 44072 55104 16895 98311 56005 23331 21939 03463 53828 78930 30987 40988 528 43473 39179 53174 43498 72674 13087 54261 01844 45738 93150 13240 16694 59155 67589 529 06513 31352 09177 21367 64725 23784 18125 74873 83971 92678 96950 69821 41119 43312 530 48734 39737 03448 99009 98136 34562 30339 93143 07350 94289 76144 47238 08110 00037 531 54832 70111 48339 75270 11652 41697 43277 58089 70520 96997 71007 87803 52458 06637 532 55844 69515 22658 75438 83086 41325 04694 40359 28351 53492 73134 02370 72313 53039 533 42829 54398 93338 90705 00626 87752 93482 27726 51835 23966 50279 26329 25754 43530 534 81128 63461 10925 44382 73365 98875 77605 27351 49177 36914 50258 62361 38229 89608 535 62885 26354 10368 78026 00186 46783 02059 98892 98061 15330 31705 71923 29266 72716 536 19525 10375 27010 42791 49471 90607 98103 31752 04842 13693 84292 48485 76178 41716 537 26570 99202 73924 59888 01827 93314 63949 35394 12989 05867 11568 45056 16609 20470 538 04772 17749 01537 96036 02102 02622 06007 52239 61201 57415 35609 38761 19589 24238 539 49129 12491 62552 64323 44856 29045 76871 80449 81351 73642 48643 23848 48390 56829 540 19937 75104 57780 95871 94547 53541 77723 54114 90290 62627 65151 15687 81062 06729 541 52571 67962 72775 28480 87411 12075 45177 08796 99297 48807 88310 75454 45456 85394 542 54943 80723 81195 84069 28144 48106 04169 16575 62665 97861 71650 56981 61794 94285 543 16375 88048 29625 08111 92924 53335 09525 88290 17679 08945 25816 11848 95106 22031 544 38745 91458 30363 95005 55854 38628 13599 73065 40870 82576 37089 86738 16284 44725 545 09937 17776 86425 88916 80594 28347 08092 64255 55604 78635 13197 72213 95102 36723 546 30097 47192 27960 15937 42080 61048 14358 44508 72683 51088 55368 75587 27046 11198 547 02410 60124 62825 42947 74590 89730 16073 28184 30078 92578 83789 08044 76238 47599 548 44804 80165 19442 72194 76910 40274 93861 06568 92482 70037 66779 63312 00619 94053 549 37352 79142 51032 58844 03167 57351 51850 92810 35331 78995 44221 41532 51606 26430 550 60640 14199 48263 71533 94235 42431 44114 90993 41149 06159 39242 11163 14764 19246 App. C-15